PROBABILITY
CLASS X
Generally in our daily life we have 3 types of situations
2. Impossible
3. Happen but not confirm
(may or may not)
Impossible
Certain
Even Chance
Unlikely
Likely
②
⑤
③
④
①
Probability is the study of chances, i.e.
Theory of probability
is
Contribution of Mathematicians
James Bernoulli (1654-1705),
A.de.Moivre(1667-1754)
Pierre simon laplace(1749-1827)
Terms of probability
Experiment
Experiment means an operation which can produce some well defined outcomes
Example : Results knowing early before doing experiments in Laboratory
Random Experiment
Examples:
The outcomes of an experiment are the ways it can happen.
The event is the particular outcome you are looking for.
6
10
2
52
Sample Space
Elementary event
If a random experiment is performed, then each outcome is known as elementary event
Sure Event: Those events whose probability is one.�Example : The probability of getting a white ball from a group of white balls.
�Impossible Event: Those events whose probability is zero.
Example :
The probability of getting a number greater than 6, when a die is thrown once, is an impossible event, as the highest number in a die is 6.�
Types of Events
Favorable event
The cases which ensure the occurrence of an event are called favorable cases to that event
The Probability of an Event is
P(Event) = Number of trails in which the event happened
Total number of trails
(OR)
P(Event) = Number of outcomes favorable to Event
Number of all possible outcomes
Complimentary events
The event Ē, representing not E is called compliment of the event E
P(Ē) = 1-P(E)
Probability of tossing a coin
Probability of Head = ½
Probability of Tail = ½
All possible outcomes of Two coins
?
H H
T T
H T
T H
Probability (Two heads) = ¼
Probability (Two tails) = ¼
Probability (one tail and one head) =2/4
= 1/2
3 Coins tossed at a time
Probability of a die
A die
2 Dice thrown at once
1,1 | 1,2 | 1,3 | 1,4 | 1,5 | 1,6 |
2,1 | 2,2 | 2,3 | 2,4 | 2,5 | 2,6 |
3,1 | 3,2 | 3,3 | 3,4 | 3,5 | 3,6 |
4,1 | 4,2 | 4,3 | 4,4 | 4,5 | 4,6 |
5,1 | 5,2 | 5,3 | 5,4 | 5,5 | 5,6 |
6,1 | 6,2 | 6,3 | 6,4 | 6,5 | 6,6 |
Probability (same number) = 6/36
Probability (Sum is 8) = 5/36
Probability (product is 100) = 0/36
Probability of playing cards
Heart
Diamond
Spade
Club
52 Playing Cards in a pack
4 Suits (Clubs, Spades, Diamonds and Hearts)
13 cards in each suit (A,2,3,4,5,6,7,8,9,10,J,K,Q)
A regular dice has the numbers 1,2,3,4,5&6
FACE CARDS
Total face cards = 12
Black face cards = 6
Red face cards = 6
P(Face cards) = 12/52
P(Black/Red face cards) = 6/52
P(Jack/King/Queen) = 4/52
P(Diamond/heart/spade/club) = 13/52
P(Black/Red cards) = 26/52
B
A
B
A
A
B
1
4
1
2
3
5
2
5
1
4
Try these…
a)
b)
P(red)
P(blue)
P(yellow or blue)
1
5
Answer is
Any number less than 1 or greater than 6.
Answer is
White, because there are more white marbles than any other colour.
Write whether each event is certain, likely, unlikely, or impossible.���1. The probability of tossing a 7on a standard six-sided die.� 2. A glass jar contains 13 red marbles. Describe the probability of picking a red marble.� 3. A glass jar contains 30 marbles. The jar has purple and red marbles. There are 4 red marbles.� a)Find the probability of picking a purple marble.�b) Find the probability of picking a red marble.
Extension Activity
Extension Activity
Prepared By
M.Sreenivasa Rao
TGT(MATHS)
JNV Banavasi, Kurnool(Dt.) A.P