Question

About 25% of those called for jury duty will find an excuse to avoid it. If 12 people are called what is the probability that all 12 will be available. (Binomial distribution)

Answer 1

Approximately
`0.032` (or, equivalently,
`3.2\%`,) assuming that the availabilities of the
`12` jurors are independent from one another.

Explanation:

The question states that the probability that a given juror is unavailable is approximately
`0.25`.

For the complement of that event, the probability that this particular juror is available would be
`1 - 0.25 = 0.75`.

Assume that the availabilities of the
`12` jurors are independent from one another. The number of available jurors would be a binomial variable with
`n = 12` and
`p = 0.75` (
`12\!` independent observations, each with a
`0.75` probability of being "available".)

Hence, the probability that all
`12` jurors are available would be:

`(0.75)^(12) * (0.25)^(0) \approx 0.032 = 3.2\%`.