Question

A swim team consists of 4 boys and 5 girls. A relay team of 4

swimmers is chosen at random from the team members. What is the probability that 3
boys are selected for the relay team given that the first selection was a girl? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

P=0.071429

Explanation:

1) if the first member of team needed is already choosen and this is a girl, then the rest members are 4 boys and 4 girls. The rest 3 positions should be choosen from that 8 persons;

2) according to the condition 3 boys should be choosen from the rest team members, but there are 4 boys+4girls. The required probability can be written as

`P=(C^3_4)/(C^3_8);`

3) finally,

`P=(C^3_4)/(C_8^3)=(4*3!*5!)/(8!)=(1)/(14)=0.07142857142857142857142857142857;`

⇔ P=0.071429.

P.S. if it is possible, check the suggested solution in other sources.