Question

A swim team consist of seven boys and four girls a relay team of four swimmers is chosen at random from the team members what is the probability that three 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 million

Answer 1

At start, we have:

- 7 boys

- 4 girls

It is given that the first selection was a girl. Since there were 4 girls, there is 3 left to be picked. So we have:

- 1 girl picked

- 7 boys to be picked

- 3 girls to be picked

We want the next 3 pickes to be boys.

The probability that the first pick will be a boy is the number of boys to be picked from over the total team left to be picked from. We have 7 boys and a total of 7 + 3 = 10 members, so:

`P_1=(7)/(10)`

Next, we want another pick of boy, but now we have got only

- 6 boys

- 3 girls

So, the probability of the second pick to be boy is:

`P_2=(6)/(9)`

And for the third, we have:

- 5 boys

- 3 girls

Probability of

`P_3=(5)/(8)`

Since we want these three to occur, the final probability is the product of them:

`P=P_1\cdot P_2\cdot P_3=(7)/(10)\cdot(6)/(9)\cdot(5)/(8)=(7)/(1)\cdot(1)/(3)\cdot(1)/(8)=(7)/(24)`

So, the answer as a fraction in the lowest form is:

`(7)/(24)`