Question

A four-person committee is chosen from a group of eight boys and six girls.

If students are chosen at random, what is the probability that the committee consists of all boys?

Answer 1

10/143

Explanation:

got 100%

Answer 2

The probability is approximately 0.0699. That's
`\displaystyle (10)/(143)` to be exact.

Explanation:

How many ways to choose four out of a total of
`8 + 6 = 14` boys and girls?

`\displaystyle {14\choose 4} = 1001`.

How many ways to choose four boys out of a total eight boys?

`\displaystyle {8\choose 4} = 70`.

What's the probability that all four persons chosen out of the pack of fourteen are boys? All 1001 ways of choosing four out of fourteen are equally likely. However, only 70 satisfy the conditions. In other words, the probability of choosing four boys out of this group of eight boys and six girls is equal to:

`\begin{aligned}&\frac{\text{Number of ways to choose four out of eight}}{\text{Number of ways to choose four out of fourteen}} \\= &(70)/(1001)\\=&  (10)/(143)\approx 0.0699\end{aligned}`.