Answer to Question #88530 in Statistics and Probability for Priggish

Question

In a class of 20 children, 4 of 9 boys and 3 of 11 girls are in the athletics team. A person from the class is chosen to be in the 'egg and spoon' race on sport day. Find the probability that the person chosen is;

a) in the athletics
b) female
c) a female member of the athletics team
d) a female or in the athletics team.

Answer 1

Possibility spaceS: the class of 20 children.

a) Event A: member of the athletics team is chosen

$$P(A)={4+3 \over 20}={7 \over 20}=0.35$$

b) Event B: female is chosen

$$P(B)={11 \over 20}=0.55$$

c) Event: a female member of the athletics team $P(A\cap B).$

There are 3 girls in the athletics team. Then

$$P(A\cap B)={3 \over 20}=0.15$$

d) Event: a female or in the athletics team $P(A\cup B)$

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)=$$

$$={7 \over 20}+{11 \over 20}-{3 \over 20}={3 \over 4}=0.75$$