Question

A swim team consists of 5 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

In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then

`10\cdot9\cdot8\cdot7=5040`

if the first member is a girl and the other three needs to be boys, the number of possibilities are

`1\cdot5\cdot4\cdot3=60`

then, divide in order to find the probability

`(60)/(5040)=(1)/(84)`