Probability�Using Words and Numbers to Describe Probability
To be able to describe probabilities using both words and numbers.
Learning Objective
Success Criteria
Look at the events described below. Can you order them from most likely to happen to least likely to happen?
Starter: Ordering Events
Event 3 is the event which is most likely to happen.
The King was born in 1948, more than 70% of the cards will be less than his age.
Event 1 is the second most likely to happen.
Half of the numbers on the dice are even and the other �half are not even.
Event 2 is the event least likely to happen.
Only one of the numbers in the bag is Bet’s age in years (unless she’s over 100 years old, then there is no card with her age) and 99 of them are not her age.
Definitions
A measure of how likely
Random
If you choose a chocolate from a new box of chocolates, you will probably not do so at random; you’ll probably choose your favourite on purpose and your least favourite will be left for last.
If you write down the name of each person in your class on a separate piece of paper of equal size, put them all in a bag, shake them around then take one out with your eyes closed, you would be picking a card at random.
Probability
If a letter is picked at random � from the letters of the alphabet, � this means that every letter has an equal chance of being picked.
an event is to happen.
Describing Probability Using Words
Probability is a measurement or description of how likely an event is to happen. We can give probability using numbers (fractions, decimals or percentages) or using words.
The terms that we use to describe the likelihood of an event are:
likely
unlikely
very unlikely
certain
very likely
even chance
impossible
Describing Probability Using Words
When the probability of an event is ‘even chance’, this means that it is as likely to happen as it is to not happen, for example:
When a coin is flipped, there is an even chance that it will land on heads.
When a dice is thrown, there is an even chance that it will land on an odd number.
If Gerald’s puppy steals his shoe, there is an even chance that it will be the left shoe.
You should be familiar with most of these words from everyday life (if not from maths lessons) but can you give a definition of ‘even chance’ or an event which has an even chance of happening?
Describing Probability Using Words
The order should be:
likely
unlikely
very unlikely
certain
very likely
even chance
impossible
Describing Probability Using Words
We can show these descriptions of probability on a probability scale:
Even chance has to be right in the middle, because it describes a situation where the probability of an event happening is exactly equal to the probability of it not happening.
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unlikely
likely
very likely
impossible
very unlikely
even chance
certain
Describing Probability Using Words
Use one of the following terms:
impossible unlikely even chance likely certain
to describe the probability in each of the following situations:
Alana writes each letter of her first name on a card, shuffles the cards then takes the top card. What is the probability that the card she takes has a letter A on it?
A dice is thrown. What is the probability that it lands �on a square number?
There are 3 red sweets, 5 green sweets and 4 yellow �sweets in a jar. When one is picked out at random, �what is the probability that it is… green?
There are 3 red sweets, 5 green sweets and 4 yellow �sweets in a jar. When one is picked out at random, �what is the probability that it is… pink?
Likely
More than half the letters in her name are ‘A’s, so she has a higher than even chance but not �a certainty.
Unlikely
1 and 4 are the square numbers, so there is a less than even chance but it is not impossible.
Unlikely
There are 12 sweets altogether so there is a less than even chance but it is not impossible.
Impossible
There are no pink sweets!
Using Numbers to Measure Probability
When an event is certain to happen, we say that its probability is 1.
For example, the probability of rolling a number greater than zero on a dice is 1.
When an event is impossible, we say that its probability is 0.
For example, the probability of a dice landing on the ceiling when it is dropped is 0.
An event with even chance is exactly as likely to happen as it is to not happen so its probability is ½.
A probability is never less than zero since an event cannot be less likely than impossible.
A probability is never more than one since an event cannot be more likely than certain.
Using Numbers to Measure Probability
We can work out numerical probabilities other than 0, ½ and 1 by looking at possible outcomes.
For example, we could describe the probability of getting a 3 when we roll a dice as unlikely, but to give it a numerical value, we need to think about how many possible outcomes there are.
When we roll a dice, there are six outcomes: 1, 2, 3, 4, 5 or 6.
In only one of these outcomes is a 3 thrown, so we say that the probability of throwing a 3 is ½.
₆
Use the same method to answer the following questions...
Using Numbers to Measure Probability
Alana writes each letter of her first name on a card, shuffles the cards then takes the top card. What is the probability that the card she takes has a letter A on it?
⅜
Because 3 of the letters in her name are ‘A’s and there are 5 letters altogether in her name.
₅
Using Numbers to Measure Probability
A dice is thrown. What is the probability that it lands �on a square number?
⅔ = ⅓
Because 2 of the numbers on a dice are square numbers (1 and 4) and there are 6 numbers altogether.
₆
Using Numbers to Measure Probability
There are 3 red sweets, 5 green sweets and 4 yellow �sweets in a jar. When one is picked out at random, �what is the probability that it is… green?
⅝
Because 5 of the sweets are green and there are �12 altogether.
₁₂
Using Numbers to Measure Probability
There are 3 red sweets, 5 green sweets and 4 yellow �sweets in a jar. When one is picked out at random, �what is the probability that it is… pink?
⅝ = 0
Because none of the sweets are pink and there are �12 altogether.
₁₂
⁰
Using Numbers to Measure Probability
What do we mean when we say that the sweet is �picked out at random?
We mean that each sweet in the bag has an equally likely chance to be picked.
Decimals and Percentages
So far, we have looked at giving probabilities using words and fractions.
Probabilities may also be given using decimals or percentages, �for example, if a probability is given as ½, it could otherwise be described as 0.5 or 50%.
Therefore, it is important to be able to convert fractions, decimals and percentages.
Activity Sheet
Now work through the exercises individually.
Plenary
Imagine that you write each letter of your first name on a piece of paper then place all of these pieces of paper (which are of equal size) in a bag and shake them around. Without looking, you pick out a slip. Why is this defined as picking at random?
�Consider the following events. Can you match these events to the probability descriptions below? Can you think of events to match the other probability descriptions?
Now find a numerical (fraction, percentage or decimal) probability for each of the events that you used.