6-Nov-26

10QQ

Images from TheNounProject.com & Gemini�GarethBell.com �

Probability Starters

6 November 2026

About

1. Made by Gareth Bell, 2025/2026 for Level 2 Probability Revision starter.
2. Date top right auto updates in ppt. �I asked my students to write the date in the top right of their book each day, just like I did.
3. To jump to a slide, run the powerpoint (e.g. F5), then type the slide number in (e.g. 47), and then press enter. I write down in my diary what slide we’re up to.
4. Every odd page is without answers for easy printing.
5. Designed to be quicker, easier versions of exam questions for easy revision/starters
6. The CQ is meant to be a challenge question (differentiated learning)

7. Slides can be categorised into Tables, Trees, Norm Distribution (with a few extra discuss distribution questions later on).
8. Images either drawn in shapes (took me a while) or from the nounproject.com so not breaking copyright.
9. I am not selling this, however, if it saves you hours of work feel free to send me a thank you message. Also let me know which resource you’re using.
10. I wanted there to be a tenth bullet point for completion ☺.

- Gareth Bell.com

6 November 2026

Norm or Inverse Norm - Revision

1. The average Llama lives 22 years with a standard deviation of 5 years.
1. How many live longer than 30?
2. How old do the bottom 15% live?
3. How many live between 20 and 30?

​

​

​

​

2. An average Llama weighs 160kg, with a stdev of 40kg.
1. How heavy to be in the top �10% of obese Llamas?
2. How heavy are the top 50%?
3. What percentage are between 100kg and 200kg?

CQ) Of 33 llamas, how many are probably 200kg or more?

3

6 November 2026

Norm or Inverse Norm - Revision

1. The average Llama lives 22 years with a standard deviation of 5 years.
1. How many live longer than 30?
2. How old do the bottom 15% live?
3. How many live between 20 and 30?

​

​

​

​

2. An average Llama weighs 160kg, with a stdev of 40kg.
1. How heavy to be in the top �10% of obese Llamas?
2. How heavy are the top 50%?
3. What percentage are between 100kg and 200kg?

CQ) Of 33 llamas, how many are probably 200kg or more?

= 5.480%

= 60.06%

= 77.45%

= 5.236 Llamas (5 llamas)

= 16.82 years

= 211.3kg

= 160kg

4

6 November 2026

Left handed - Tables Revision

1. What is the missing number x?
2. How many left-handed people participated?
3. What is the probability that a person is left-handed?
4. What is the probability that a person is left-handed given that they have a left-handed Mum?
5. What is the probability that a person is left-handed and have a left-handed Mum?
6. What is the probability that a person is left-handed or have a left-handed Mum?
7. How much more likely are left-handed mothers to have a left-handed child than right-handed mothers?

​

6 November 2026

Left handed - Tables Revision

1. What is the missing number x?
2. How many left-handed people participated?
3. What is the probability that a person is left-handed?
4. What is the probability that a person is left-handed given that they have a left-handed Mum?
5. What is the probability that a person is left-handed and have a left-handed Mum?
6. What is the probability that a person is left-handed or have a left-handed Mum?
7. How much more likely are left-handed mothers to have a left-handed child than right-handed mothers?

​

= 395

= 39

L) 18/160 (11.25%)

R) 21/273 (7.692%)

L ÷ R = 1.463 times

6 November 2026

Tables Revision - Subway

Oliver eats Subway ¾ of the time. No matter where he goes, �he always gets Chicken 80% of the time. Fill in the tree:

1. What is the probability that Oliver gets Meatball?
2. What is the probability that Oliver gets Chicken?
3. What is the chance Oliver gets Chinese Chicken?
4. What is the chance Oliver gets Chicken or Chinese

7

6 November 2026

Tables Revision - Subway

Oliver eats Subway ¾ of the time. No matter where he goes, �he always gets Chicken 80% of the time. Fill in the tree:

1. What is the probability that Oliver gets Meatball?
2. What is the probability that Oliver gets Chicken?
3. What is the chance Oliver gets Chinese Chicken?
4. What is the chance Oliver gets Chicken or Chinese

80%

80%

20%

20%

8

15%

80%

20%

85%

6 November 2026

Norm or Inverse Norm - Revision

1. Female Axolotl weighs 175g (ave) with a standard deviation of 50g.
1. How many weigh less than 100g?
2. How big are the top 15%?
3. How many weigh 150 – 200g?

​

​

​

​

2. An average axolotl is 23cm long with standard deviation of 4cm
1. How long are the�10% smallest Axolotl?
2. How long are the top 84.1%?
3. What percentage are between 10cm and 20cm?

CQ) If there are 500 Axolotls in NZ, is there likely to be one 30cm long?

9

6 November 2026

Norm or Inverse Norm - Revision

1. Female Axolotl weighs 175g (ave) with a standard deviation of 50g.
1. How many weigh less than 100g?
2. How big are the top 15%?
3. How many weigh 150 – 200g?

​

​

​

​

2. An average axolotl is 23cm long with standard deviation of 4cm
1. How long are the�10% smallest Axolotl?
2. How long are the top 84.1%?
3. What percentage are between 10cm and 20cm?

CQ) If there are 500 Axolotls in NZ, is there likely to be one 30cm long?

= 0.06681

= 0.3829

= 0.2261

P(z>30) = 0.04006

0.04006x500 = 20

Yes, about 20

​

= 226.8g

= 17.87cm

= 19cm

10

6 November 2026

Axolotyl - Tables Revision

1. What is the missing number x?
2. How many girls people participated?
3. What is the probability that a person likes Axoltol?
4. What is the probability that a person likes Axolotl given that they are a boy?
5. What is the probability that a person likes Axolotl and are a boy?
6. What is the probability that a person likes Axolotl�or are a boy?
7. How many times more likely are girls liking Axolotl �than boys liking Axolotl?

​

6 November 2026

Axolotyl - Tables Revision

1. What is the missing number x?
2. How many girls people participated?
3. What is the probability that a person likes Axoltol?
4. What is the probability that a person likes Axolotl given that they are a boy?
5. What is the probability that a person likes Axolotl and are a boy?
6. What is the probability that a person likes Axolotl�or are a boy?
7. How many times more likely are girls liking Axolotl �than boys liking Axolotl?

​

= 63

= 70

G) 42/70 (60%)

B) 28/63 (44.444%)

G ÷ B = 1.35 times

6 November 2026

Trees Revision - Dragons

Stella plays the game “Axolotl or Dragon”. A dragon is shown 40% of the time, in which case she guesses correctly 3/8 of the time. She always guesses Axolotls correctly.

1. P (Dragon & Wrong)?�
2. P (Axolotl & Wrong)?�
3. P (Dragon)?
4. P (Correct)?

​

CQ) If it’s a dragon, how much more likely is she to be wrong? �

​

13

6 November 2026

Trees Revision - Dragons

Stella plays the game “Axolotl or Dragon”. A dragon is shown 40% of the time, in which case she guesses correctly 3/8 of the time. She always guesses Axolotls correctly.

3/8

100%

0%

5/8

60%

14

= 25%

= 0%

= 40%

= 15% + 60%

=75%

15%

25%

60%

0

= 25% ÷ 15%

=1.667

1. P (Dragon & Wrong)?�
2. P (Axolotl & Wrong)?�
3. P (Dragon)?
4. P (Correct)?

​

CQ) If it’s a dragon, how much more likely is she to be wrong? �

​

6 November 2026

Tables – Honey toast?

Harry tracks his toast toppings for a month

1. What is the missing number x?
2. How many weekdays were there?
3. What’s chance he has honey on a random day?
4. It’s a weekday, What’s the chance he has honey?
5. What’s the chance a random day is a weekday �that he has honey?
6. What’s the chance it is a weekday, or he has honey?
7. How much more likely is he to have honey on a weekend than a weekday?

​

6 November 2026

Tables – Honey toast?

Harry tracks his toast toppings for a month

1. What is the missing number x?
2. How many weekdays were there?
3. What’s chance he has honey on a random day?
4. It’s a weekday, What’s the chance he has honey?
5. What’s the chance a random day is a weekday �that he has honey?
6. What’s the chance it is a weekday, or he has honey?
7. How much more likely is he to have honey on a weekend than a weekday?

​

= 13

= 21

WD) 7/21 or 1/3

WE) 6/9 or 2/3

WE ÷ WD = 2 times

6 November 2026

Trees Revision - Honey-wall

Ella plays the game “Honey Stick”. The Honey-toast sticks to the wall 73% of the time. If it sticks to the wall, it stays forever 0.1 of the time, it falls 0.3 of the time, otherwise Mum gets angry.

1. P (Sticks forever)?�
2. P (Stick & Angry)?�
3. P (Falls)?
4. P (Forever or Angry)?

​

CQ) Is Angry 5 times more likely than sticks Forever?

​

6 November 2026

Trees Revision - Honey-wall

Ella plays the game “Honey Stick”. The Honey-toast sticks to the wall 73% of the time. If it sticks to the wall, it stays forever 0.1 of the time, it falls 0.3 of the time, otherwise Mum gets angry.

1. P (Sticks forever)?�
2. P (Stick & Angry)?�
3. P (Falls)?
4. P (Forever or Angry)?

​

CQ) Is Angry 5 times more likely than sticks Forever?

​

0.1

0.3

27%

18

= 7.3%

= 43.8%

= 48.9%

= 7.3% + 43.8%

=51.1%

0.6

7.3%

21.9%

43.8%

= 43.8% ÷ 7.3%

=6 (no it’s 6)

27%

6 November 2026

Norm Revision – Honey Machine

1. The honey dispenser spurts out 304grams of honey on average, with a deviation of 2 grams.
1. Probability it weighs less than 300g?
2. How big are the top 50%?
3. How many weigh 300 – 310g?

​

​

​

​

2. Honey has about 82 grams of sugar per 100g with Std dev of 3g
1. How much sugar per 100g in the bottom 10% of jars?
2. How many have more than 90g?
3. What percentage are between 80g and 90g?

CQ) If I have 50 jars, �how many have less than 80g?

19

6 November 2026

Norm Revision – Honey Machine

1. The honey dispenser spurts out 304grams of honey on average, with a deviation of 2 grams.
1. Probability it weighs less than 300g?
2. How big are the top 50%?
3. How many weigh 300 – 310g?

​

​

​

​

2. Honey has about 82 grams of sugar per 100g with Std dev of 3g
1. How much sugar per 100g in the bottom 10% of jars?
2. How many have more than 90g?
3. What percentage are between 80g and 90g?

CQ) If I have 50 jars, �how many have less than 80g?

= 0.02275

= 0.9759

= 0.7437

P(z<80) = 0.2525

0.2525x60 = 15

15 jars

​

= 304g

= 78.16g

= 0.00383

20

6 November 2026

Tables – Powers

Riley compares the powers of DC and Marvel

1. What is the missing number x?
2. How many Marvel heroes were there?
3. Probability a random hero is Marvel and Strong?
4. I am a Marvel hero, What’s the chance I can fly?
5. What’s the chance a random hero is DC or can fly?
6. How many Marvel people are strong?
7. Are Marvel heroes twice as likely to be strong �than DC heroes?

​

6 November 2026

Tables – Powers

Riley compares the powers of DC and Marvel

1. What is the missing number x?
2. How many Marvel heroes were there?
3. Probability a random hero is Marvel and Strong?
4. I am a Marvel hero, What’s the chance I can fly?
5. What’s the chance a random hero is DC or can fly?
6. How many Marvel people are strong?
7. Are Marvel heroes twice as likely to be strong �than DC heroes?

​

= 9

= 10

= 7

Marvel =0.7

DC = 0.4545

0.7 ÷ 0.4545 = 1.54 times

No, they’re not

9

6 November 2026

Trees Revision - Batman

Batman drives the Batmobile to 80% of events, Batboat for 10%, and also sometimes flies. If he drives he arrives safely 3/5 of the time, if he flies he arrives safely 1/3 the time, and if he takes the boat he is unsafe.

1. P(Drive & Unsafe)�
2. P (Fly & Safe)�
3. P (Safe)?�
4. P (Drive & unsafe, �OR flies)?

CQ) If he arrived safely, what is the probability that he drove?

​

Safe

Unsafe

Safe

Unsafe

6 November 2026

Trees Revision - Batman

Batman drives the Batmobile to 80% of events, Batboat for 10%, and also sometimes flies. If he drives he arrives safely 3/5 of the time, if he flies he arrives safely 1/3 the time, and if he takes the boat he is unsafe.

1. P(Drive & Unsafe)�
2. P (Fly & Safe)�
3. P (Safe)?�
4. P (Drive & unsafe, �OR flies)?

CQ) If he arrived safely, what is the probability that he drove?

​

Safe

Unsafe

Safe

Unsafe

10%

10%

3/5

2/5

1/3

2/3

0

1

= 0.48

= 0.32

= 0

= 0.1

= 0.0333

= 0.0667

= 0.32

= 0.03333

= 0.48 + 0 � + 0.0333�= 0.5133

= 0.32 + 0.1�=0.42

0.48 ÷ (0.48 + 0.0333) = 0.9351

6 November 2026

Norm Revision – Batmobile

1. Batman puts an average of 56 litres of fuel into the batmobile, with a standard deviation of 2.
1. Probability he runs out �(needs more than 60L)?
2. Probability he puts in 50-60L?
3. How little is the lowest 5%?

​

​

​

​

2. “91 pumps” have 91% octane in it, with a standard deviation of 1%
1. P(z > 90%)?
2. P it has less than 88%
3. How much octane in the �highest 10% of pumps?

CQ) If Levin has 35 fuel pumps how many will have At least 90% octane?

25

6 November 2026

Norm Revision – Batmobile

1. Batman puts an average of 56 litres of fuel into the batmobile, with a standard deviation of 2.
1. Probability he runs out �(needs more than 60L)?
2. Probability he puts in 50-60L?
3. How little is the lowest 5%?

​

​

​

​

2. “91 pumps” have 91% octane in it, with a standard deviation of 1%
1. P(z > 90%)?
2. P it has less than 88%
3. How much octane in the �highest 10% of pumps?

CQ) If Levin has 35 fuel pumps how many will have At least 90% octane?

= 0.02275

= 52.71 litres

= 92.28% octane

P(z>90) = 0.8413%

0.8413x35 = 29.44

29 pumps

​

= 0.9759

= 84.13%

= 0.135%

26

6 November 2026

Tables – Sleepy Sam

1. Which of the bold numbers is wrong?
2. Is he twice as likely to sleep in during �Term Time (8) than holidays (4)?
3. P(sleeps in)
4. P(it is a holiday)
5. What is the chance he sleeps in given that it’s a holiday?
6. If he slept in, what’s the chance it is holidays?
7. How many times more likely is he to sleep in during holidays than term time?

​

6 November 2026

Tables – Sleepy Sam

1. Which of the bold numbers is wrong?
2. Is he twice as likely to sleep in during �Term Time (8) than holidays (4)?
3. P(sleeps in)
4. P(it is a holiday)
5. What is the chance he sleeps in given that it’s a holiday?
6. If he slept in, what’s the chance it is holidays?
7. How many times more likely is he to sleep in during holidays than term time?

​

= 34 should be 66

= no (see Q7)

P(Sleep in during holidays) = 0.25 (4/16),

P(sleep in during term time) = 0.16 (8/50)

0.25 ÷ 0.16 = 1.56 times more likely

6 November 2026

Trees Revision – Kittens online

Addy spends 40% of their phone time on Tiktok, and splits the rest evenly between IG and Youtube. When on Tiktok or IG, Kittens appear a third of the time, and on Youtube, there are no kittens 4/5 of the time

1. P(IG & Kittens)
2. P(TikTok & No kittens)�
3. P(Kittens)?�
4. P not(youtube and kittens)?

CQ) If there were kittens, what’s the chance of �it being on TikTok?

​

Kittens

No Kittens

Kittens

No Kittens

6 November 2026

Trees Revision – Kittens online

Addy spends 40% of their phone time on Tiktok, and splits the rest evenly between IG and Youtube. When on Tiktok or IG, Kittens appear a third of the time, and on Youtube, there are no kittens 4/5 of the time

30%

30%

1/3

2/3

1/5

4/5

1/3

2/3

= 0.1333

= 0.2667

= 0.1

= 0.2

= 0.06

= 0.24

= 0.1

= 0.2667

= 0.1333 � + 0.1 + 0.06�= 0.2933

= 1 – 0.06�=0.94

0.1333 ÷ (0.2933) �= 0.4545

Kittens

No Kittens

Kittens

No Kittens

1. P(IG & Kittens)
2. P(TikTok & No kittens)�
3. P(Kittens)?�
4. P not(youtube and kittens)?

CQ) If there were kittens, what’s the chance of �it being on TikTok?

​

6 November 2026

Norm Revision – Kitten Reels

1. My Kitten reels last an average of 12 sec, �with a standard deviation of 2.5 sec.
1. Probability a reel is longer than 14 sec?
2. Probability a reel is 5 sec or longer?
3. To be longest 10%, how long?

​

​

​

​

2. My Kitten sleeps like a bell curve, around 20 hours per day, �with standard dev of 1 hour.
1. P(z > 19.5 hours)?
2. How much sleep does she get �min in the ¼ most sleepy days?
3. P(19-22 hours)?

CQ) How many days a week does she sleep more than 20 hours 20 min?

31

6 November 2026

Norm Revision – Kitten Reels

1. My Kitten reels last an average of 12 sec, �with a standard deviation of 2.5 sec.
1. Probability a reel is longer than 14 sec?
2. Probability a reel is 5 sec or longer?
3. To be longest 10%, how long?

​

​

​

​

2. My Kitten sleeps like a bell curve, around 20 hours per day, �with standard dev of 1 hour.
1. P(z > 19.5 hours)?
2. How much sleep does she get �min in the ¼ most sleepy days?
3. P(19-22 hours)?

CQ) How many days a week does she sleep more than 20 hours 20 min?

= 0.2119

= 0.8186

= 15.2 sec

= 0.6915

= 20.67 hours

32

= 0.9974

P(z>20.333) = 0.3695

0.3695 × 7 = 2.587

2 or 3 days

​

6 November 2026

Tables – Chaotic Kittens

1. What is the missing number?
2. Of the adult cats, what is the probability it is sleeping?
3. I see a sleeping feline, what’s the probability it’s a kitten?
4. Probability a feline is Sleeping or being Chaotic?
5. Probability a feline is a kitten or chilling?
6. Probability a random Kitten is chilling?
7. If there are 63 Kittens in my town, on average, at any given time, how many are causing chaos?

​

6 November 2026

Tables – Chaotic Kittens

1. What is the missing number?
2. Of the adult cats, what is the probability it is sleeping?
3. I see a sleeping feline, what’s the probability it’s a kitten?
4. Probability a feline is Sleeping or being Chaotic?
5. Probability a feline is a kitten or chilling?
6. Probability a random Kitten is chilling?
7. If there are 63 Kittens in my town, on average, at any given time, how many are causing chaos?

​

= 8

=3 ÷ 24 × 63

= 7.875

= 7 or 8 kittens

6 November 2026

Trees Revision – Pibble

You see Geeble Pibbles about 10% of the time. Bagel Pibbles are always cute, only half of Geeble Pibbles are cute, and Washingtons are ugly 0.3 of the time.

1. P(Cute & Geeble)
2. P(Ugly)? �
3. P(Cute or �Geeble)
4. If it is Cute, P(Geeble)?

CQ) If Ugly, How much more likely to be a Washington?

​

Cute

Ugly

Cute

Ugly

6 November 2026

Trees Revision – Pibble

You see Geeble Pibbles about 10% of the time. Bagel Pibbles are always cute, only half of Geeble Pibbles are cute, and Washingtons are ugly 0.3 of the time.

1. P(Cute & Geeble)
2. P(Ugly)? �
3. P(Cute or �Geeble)
4. If it is Cute, P(Geeble)?

CQ) If Ugly, How much more likely to be a Washington?

​

Cute

Ugly

Cute

Ugly

10%

40%

1

0

0.7

0.3

1/2

1/2

= 0.5

= 0

= 0.05

= 0.05

= 0.28

= 0.12

= 0.05

=0 + 0.05 + 0.12

= 0.17

= 0.5 + 0.05 + 0.05 + 0.28�= 0.88

= 0.05 ÷ 0.83�=0.06024

= 12 ÷ 5

= 2.4 times

1

0

6 November 2026

Norm Revision – Dinosaurs

1. The Diplodocus grew to an average �of 27m, with a standard deviation of 1.5m.
1. Probability it is longer 25m?
2. Probability it is shorter than 30m?
3. To be shortest 10%, how long?

​

​

​

​

2. A T-Rex eats about 140kg of �meat per day, with a standard deviation of 70kg.
1. What is the chance �it doesn’t eat in a day?
2. How much food in the biggest �day of the week (top 1/7^th) ?

CQ) How many days a year does �he eat more than 200kg?

6 November 2026

Norm Revision – Dinosaurs

1. The Diplodocus grew to an average �of 27m, with a standard deviation of 1.5m.
1. Probability it is longer 25m?
2. Probability it is shorter than 30m?
3. To be shortest 10%, how long?

​

​

​

​

2. A T-Rex eats about 140kg of �meat per day, with a standard deviation of 70kg.
1. What is the chance �it doesn’t eat in a day?
2. How much food in the biggest �day of the week (top 1/7^th) ?

CQ) How many days a year does �he eat more than 200kg?

= 0.9088

= 25.08m

= 0.02275

= 214.7kg

38

= 0.9772

P(z>200) = 0.1957

0.1957 × 365 = 71.42

= 71 days (72 in a leap year)

​

6 November 2026

Tables Revision – Pabbles ^{(Pibble-Tables)}

1. Of the tiktok videos, what probability of ‘potato’?
2. Of the wash my belly videos, �What is the probability it is on tiktok?
3. Probability a video is on youtube and a potato?
4. Probability a video is youtube or Potato?
5. Probability a video is on youtube, �given that it is a potato video?

CQ) If I watch 8 different Pibble videos, how �many would probably be ‘Wash my belly’?

​

6 November 2026

Tables Revision – Pabbles ^{(Pibble-Tables)}

1. Of the tiktok videos, what probability of ‘potato’?
2. Of the wash my belly videos, �What is the probability it is on tiktok?
3. Probability a video is on youtube and a potato?
4. Probability a video is youtube or Potato?
5. Probability a video is on youtube, �given that it is a potato video?

CQ) If I watch 8 different Pibble videos, how �many would probably be ‘Wash my belly’?

​

26 ÷ 40 × 8

= 5.2

About 5 videos

6 November 2026

Trees Revision – Heart Attack

About 40% of heart attacks come with no noticed warning. About 2/3 of heart attacks occur in men, and about 10% of heart attacks are immediately fatal.

4. What portion of fatal heart attacks are in men?

CQ) Out of 118 fatal heart attacks in Levin, how many are likely women?

​

​

Men

Women

1. P(warning, man, fatal)
2. P (Fatal)?
3. Probability that a �random heart attack �is fatal and in a man?

6 November 2026

Trees Revision – Heart Attack

About 40% of heart attacks come with no noticed warning. About 2/3 of heart attacks occur in men, and about 10% of heart attacks are immediately fatal.

4. What portion of fatal heart attacks are in men?

CQ) Out of 118 fatal heart attacks in Levin, how many are likely women?

​

​

Men

Women

60%

2/3

1/3

2/3

1/3

10%

90%

10%

90%

10%

90%

10%

90%

= 0.02667

= 0.24

= 0.01333

= 0.12

= 0.04

= 0.36

= 0.02

= 0.18

1. P(warning, man, fatal)
2. P (Fatal)?
3. Probability that a �random heart attack �is fatal and in a man?

= 0.04

= 0.1

= 0.02667 + 0.04

= 0.06667

= 0.0333 ÷ 0.1 × 118�= ~39 people

6 November 2026

Norm Revision – Cig vs Vape

1. Blueberry vapes have an average of 20mg of nicotine per ml, with standard deviation of 4mg.
1. How much nicotine in the �least poisonous 25% of vapes?
2. Probability it has more than 25mg?
3. Probability it has more than 30mg?
4. To be the 1/6^th most, how much?

​

​

​

​

2. A 20pack of cigarettes has about 22mg of nicotine, with st dev of 2mg.
1. How much nicotine in the �least poisonous 25%
2. Probability it has more than 25mg?

CQ) Which is most poisonous?

6 November 2026

Norm Revision – Cig vs Vape

1. Blueberry vapes have an average of 20mg of nicotine per ml, with standard deviation of 4mg
1. How much nicotine in the �least poisonous 25% of vapes?
2. Probability it has more than 25mg?
3. Probability it has more than 30mg?
4. To be the 1/6^th most, how much?

​

​

​

​

2. A 20pack of cigarettes has about 22mg of nicotine, with st dev of 2mg
1. How much nicotine in the �least poisonous 25%
2. Probability it has more than 25mg?

CQ) Which is most poisonous?

= 17.30mg

= 0.1056

= 0.006210

= 23.87mg

= 20.65mg

= 0.06681

= Cigarettes �on average

6 November 2026

Distribution – Hours of Study

This data is not normal.

Prove it, and describe it

Hours of Study

0 1 2 3 4 5 6 7 8

🡨 Mean

🡨 Median

45

6 November 2026

Distribution – Hours of Study

This data is not normal.

Prove it, and describe it

1. Symmetry/skew��
2. Central Cluster�
3. Falls Away�
4. Outliers
5. Overall
6. Description meaning:

= not symmetrical, �right skew

= Mean is to the right of median, not norm.

= Steep drop off on both sides,

= Maybe Outliers on the far right.

= Not norm, Right skewed.

Hours of Study

0 1 2 3 4 5 6 7 8

🡨 Mean

🡨 Median

= Not norm, Right skewed. Which means a few people study a lot, but most study not much at all.

6 November 2026

Tables Revision – Ben’s Bread

Benny tracks what toppings on his breakfast for a month

1. How many days did he have Toast?
2. P(jam on toast)?
3. P(avo on bread)?
4. Probability of Jam, given that he is having toast?
5. Probability of jam or toast?

CQ) Benny’s Mum claims that if he has bread, �then he is three times as likely to have � jam. Is this true?

CCQ) What month is this for?

​

6 November 2026

Tables Revision – Ben’s Bread

Benny tracks what toppings on his breakfast for a month

1. How many days did he have Toast?
2. P(jam on toast)?
3. P(avo on bread)?
4. Probability of Jam, given that he is having toast?
5. Probability of jam or toast?

CQ) Benny’s Mum claims that if he has bread, �then he is three times as likely to have � jam. Is this true?

CCQ) What month is this for?

​

= 19 days

= 0

= February (29 days)

Jam&bread 3/10 = 0.3

Jam&toast 2/19 = 0.1053

Yes, about 3 times as likely

6 November 2026

Trees Revision – Sleep late

Oli stays up late 75% of the time. If he stays up late, he sleeps in 4/5 of the time otherwise, just 2/5. If he sleeps in, he is late to school 60% of the time, if he wakes on time, he is never late.

CQ1) What portion of �‘On Time to School’ �are after Sleep ins?

CQ2) Out of 50 mornings �in a term, how many times late?

​

​

Sleep in

Wake �on time

1. P(Stay up late, sleep in, on time)?
2. P(bed on time, sleeps in)?
3. Probability that a �Oli is late to school?
4. Probability Oli sleeps in?

6 November 2026

Trees Revision – Sleep late

Oli stays up late 75% of the time. If he stays up late, he sleeps in 4/5 of the time otherwise, just 2/5. If he sleeps in, he is late to school 60% of the time, if he wakes on time, he is never late.

CQ1) What portion of �‘On Time to School’ �are after Sleep ins?

CQ2) Out of 50 mornings �in a term, how many times late?

​

​

Sleep in

Wake �on time

25%

4/5

1/5

2/5

3/5

60%

40%

0

1

60%

40%

0

1

= 0.36

= 0.24

= 0

= 0.15

= 0.06

= 0.04

= 0

= 0.15

1. P(Stay up late, sleep in, on time)?
2. P(bed on time, sleeps in)?
3. Probability that a �Oli is late to school?
4. Probability Oli sleeps in?

= 0.24

= 0.10

= 0.36 + 0.06�= 0.42

= sleep in on time ÷ on time

= (0.24 + 0.04) � ÷ 0.24 + 0.15 + 0.04 + 0.15�= 0.28 ÷ 0.58

= 0.4828

= 0.42 × 50�= 21 mornings

= 0.60 + 0.1�= 0.7

6 November 2026

Norm Revision – Sleep

1. Year 12s sleep on average of 7 hours a night, with a standard deviation of 2/3 an hour.
1. How much sleep, do the least 15% get?
2. P(at least 8 hours)?
3. P(under 6 hours)?
4. To be the top 10%, how much?

CQ) Out of 23 year 12s, how many�probably had over 7.5 hours sleep?

​

​

​

2. Teenagers are recommended to get around 9 hours sleep, with a standard deviation of 0.5 hours
1. How much sleep, do the top 20% need?
2. What % need at least 10 hours?

6 November 2026

Norm Revision – Sleep

1. Year 12s sleep on average of 7 hours a night, with a standard deviation of 2/3 an hour.
1. How much sleep, do the least 15% get?
2. P(at least 8 hours)?
3. P(under 6 hours)?
4. To be the top 10%, how much?

CQ) Out of 23 year 12s, how many�probably had over 7.5 hours sleep?

​

​

​

2. Teenagers are recommended to get around 9 hours sleep, with a standard deviation of 0.5 hours
1. How much sleep, do the top 20% need?
2. What % need at least 10 hours?

= 6.3 hours

= 0.06681

= 0.06681

= 7.854 hours

= 9.421 hours

= 2.275%

= 23 × 0.2266

= ~ 5 students

6 November 2026

Discuss Distribution – All Blacks

Analyse this data, �to see if it is normal:

Mean: 107

Median: 108

6 November 2026

Discuss Distribution – All Blacks

Analyse this data, �to see if it is normal:

1. Symmetry/skew��
2. Central Cluster��
3. Falls Away�
4. Outliers
5. Overall

Mean: 107

Median: 108

= Reasonably symmetrical, slightly left skew

= Mean is similar to median, so reasonably normal

= Steep drop off on both sides,

= Two outliers on the far right.

= Close to Norm Distributed. �A little left skewed with two outliers on right.

6 November 2026

Tables Revision – Costume Comp

Kids’ Costumes this November

1. What is the mistake in the table?
2. P(Spiderman and boy)?
3. P(spiderman or a boy)?
4. P(Spiderman given that it’s a boy)?
5. If 100 kids dress up, how many Supermarios?

CQ) Are girls over three times as likely �to dress as Toy Story than boys?

6 November 2026

Tables Revision – Costume Comp

Kids’ Costumes this November

1. What is the mistake in the table?
2. P(Spiderman and boy)?
3. P(spiderman or a boy)?
4. P(Spiderman given that it’s a boy)?
5. If 100 kids dress up, how many Supermarios?

CQ) Are girls over three times as likely �to dress as Toy Story than boys?

= 8�Toy Stories

6 November 2026

Trees Revision – Dreams

Stay up late

Bed on time

Dream

No Dream

35%

Unicorns

Unicorns

No Unicorns

No Unicorns

e) Out of 50 mornings �how many unicorns?

CQ How much more likely to have unicorns when going to bed on time compared to late nights?

​

​

Dream

No Dream

1. P(Bed on time, Dream, unicorns)?
2. P(bed on time, no dreams)?
3. Probability of unicorns?
4. P(bed on time, �& no unicorns)?

​

6 November 2026

Trees Revision – Dreams

e) Out of 50 mornings �how many unicorns?

CQ How much more likely to have unicorns when going to bed on time compared to late nights?

​

​

Dream

No Dream

1. P(Bed on time, Dream, unicorns)?
2. P(bed on time, no dreams)?
3. Probability of unicorns?
4. P(bed on time, �& no unicorns)?

​

6 November 2026

65%

30%

70%

30%

70%

= 0.042

= 0.098

= 0.21

= 0.1365

= 0.3185

= 0.195

= 0.1365

= 0.195

= 0.042 + 0.1365�= 0.1785

= 50 × (0.1365+0.042)

= 50 × 0.1785

= 9 mornings

On time:�0.1365÷0.65 = 0.21

Late: �0.042÷0.35 = 0.12

1.75 times as likely

= 0.1385

Oops, you’ve got to the end.

Options:

• Get the latest version from garethbell.com
• Go back to the start.
• Email me garethbell.com/contact to say make more �(it would be good feedback to know if people have used them all)

6 November 2026

Tables – Honey toast?

Harry tracks his toast toppings for a month

1. What is the missing number x?
2. How many weekdays were there?
3. What’s chance he has honey on a random day?
4. It’s a weekday, What’s the chance he has honey?
5. What’s the chance a random day is a weekday �that he has honey?
6. What’s the chance it is a weekday, or he has honey?
7. How much more likely is he to have honey on a weekend than a weekday?

​

= 13

= 21

WD) 7/21 or 1/3

WE) 6/9 or 2/3

WE ÷ WD = 2 times

6 November 2026

Trees Revision - Honey-wall

Ella plays the game “Honey Stick”. The Honey-toast sticks to the wall 73% of the time. If it sticks to the wall, it stays forever 0.1 of the time, it falls 0.3 of the time, otherwise Mum gets angry.

1. P (Sticks forever)?�
2. P (Stick & Angry)?�
3. P (Falls)?
4. P (Forever or Angry)?

​

​

0.1

0.3

27%

61

= 7.3%

= 43.8%

= 48.9%

= 7.3% + 43.8%

=51.1%

0.6

7.3%

21.9%

43.8%

27%

6 November 2026

Norm Revision – Honey Machine

1. The honey dispenser spurts out 304grams of honey on average, with a deviation of 2 grams.
1. Probability it weighs less than 300g?
2. How big are the top 50%?
3. How many weigh 300 – 310g?

​

​

​

​

2. Honey has about 82 grams of sugar per 100g with Std dev of 3g
1. How much sugar per 100g in the bottom 10% of jars?
2. How many have more than 90g?
3. What percentage are between 80g and 90g?

= 0.02275

= 0.9759

= 0.7437

= 304g

= 78.16g

= 0.00383

62

6 November 2026