Question

A jury pool consists of 35 people, 12 men and 23 women. Compute the probability that a randomly selected jury of 12 people is all male.

Answer 1

Based on the concept of combinations, the probability that a randomly selected jury of 12 people is all male is approximately 0.0000181, or 0.00181%.

The total number of the jury pool = 35

The number of men = 12

The number of women = 23

The total number of ways to choose 12 people from a pool of 35 is given by the combination formula:

`[ \text{Total combinations} = \binom{35}{12} ]`

The number of ways to choose 12 men from 12 men is given by the combination formula:

`[ \text{Combinations of 12 men} = \binom{12}{12} ]`

The probability of selecting 12 men is then given by the ratio of the number of ways to choose 12 men to the total number of combinations:

`[ \text{Probability} = \frac{\binom{12}{12}}{\binom{35}{12}} ]`

Evaluating this expression gives us the probability that a randomly selected jury of 12 people is all male.

`[ \text{Probability} = \frac{1}{\binom{35}{12}} ]`

The total number of combinations is given by:

`[ \binom{35}{12} = (35!)/(12!(35-12)!) = 5,527,071 ]`

The number of ways to choose 12 men from 12 men is given by:

`[ \binom{12}{12} = (12!)/(12!(12-12)!) = 1 ]`

So, the probability of selecting 12 men from the pool is:

`[ \text{Probability} = (1)/(5,527,071) \approx 0.000000181 ]`

Thus, the probability that a randomly selected jury of 12 people is all male is approximately 0.0000181, or 0.00181%.