Question

Annie and her friends start a Doubles Club. The numbers below show information about all the members of the club. Boys Girls Juniors 6 8 Seniors 16 12 Express the probability that Annie chooses a girl or a junior. Use the formula: P(AUB)= P(A)+P(B)- P(AnB)

Answer 1

Answer:
`(13)/(21)`

Explanation:

The given table :

Boys Girls

Juniors 6 8

Seniors 16 12

Let G denote the event of choosing girl and J denote the event of choosing Junior.

Number of girls : 8+12=20

Number of Juniors : 6+8=14

Members that are girl and junior = 8

Total students : 6+8+16+12=42

The probability of choosing girl is given by :-

`P(G)=(20)/(42)`

The probability of choosing junior is given by :-

`P(J)=(14)/(42)`

The probability of choosing a girl and junior is given by ;-

`P(G\cap J)=(8)/(42)`

Now, the probability choosing a girl or a junior is given by :-

`P(G\cup J)=P(G)+P(J)-P(G\cap J)\\\\=(20)/(42)+(14)/(42)-(8)/(42)\\\\=(26)/(42)=(13)/(21)`

Hence, the probability that Annie chooses a girl or a junior=
`(13)/(21)`