Probability of combined events
Contents
- Dependent & Independent Events
- Example of Tree Diagram
- Example of Possibility Diagram
- Example of Addition and Multiplication of Probabilities
Dependent & Independent Events
Dependent Events – Happening of one event affect another.
In throwing a dice, the event of getting an odd number affect the event of getting an even number, so they are dependent events.
Independent Events – Happening of one event does not affect another.
In tossing a coin and throwing a dice outcomes does not affect each other, so they are independent events.
Example
There are 9 yellow balls, 4 red balls and 3 blue balls in a bag. A ball is drawn, color noted and replaced in the bag. Find the probability of picking a red ball followed by a blue ball?
First ball is replaced in the bag before drawing Second ball
Total number of balls = 9 + 4 + 3 = 16
Probability of picking a red ball is 4/16 = ¼
Probability of picking a blue ball is 3/16
Hence the probability of picking a red ball and blue ball with replacing = (1/4) x (3/16) = 3/64
First ball is NOT replaced in the bag before drawing Second ball
Total number of balls = 9 + 4 + 3 = 16
Probability of picking a red ball is 4/16 = ¼
Probability of picking a blue ball is 3/15 = 1/5
Hence the probability of picking a red ball and blue ball with replacing = (1/4) x (1/5) = 1/20
Example of Tree Diagram
Box A has three balls numbered 1, 3, 4 and box B has two balls numbered 3, 5. A ball is picked at random from each box. With the help of a tree diagram, find the product of numbers in both balls is (a) odd (b) even.
Example of Possibility Diagram
Box A has four balls numbered 1, 3, 4, 6 and box B has three balls numbered 2, 3, 5. A ball is picked at random from each box. With the help of a possibility diagram find the sum of numbers in both balls is (a) odd (b) even.
Example
Two dice are thrown and the numbers that appear are multiplied.
Find the probability that the product is
- an odd number
- a number less than 10
- a number that is a multiple of 6
P (odd number) = 9/36 = 1/4
P (number less than 10) = 17/36
p (number that is a multiple of 6) = 15/36 = 5/12
Example of Addition and Multiplication of Probabilities
On any day, the probability that James will be late for school is 1/8. Find the probability that he
- will not be late on a particular day
- will be late on two particular consecutive days
- will be late on just one of two particular consecutive days
P (James will not be late on particular day) = 1 - 1/8 = 7/8
P (James will be late on two particular consecutive days) = (1/8) x (1/8) = 1/64
P (James will be late on just one of two particular consecutive days) = (1/8) x (7/8) + (7/8) x (1/8) = 7/64 + 7/64 = 14/64 = 7/32
questions
In a class there are 20 boys and 25 girls. Two students are selected from the class one after another. Find the probability that
(i) both of them are boys
(ii) both of them are girls
(iii) first one is a girl and second one is a boy