Answer:
Approximately [tex]0.032[/tex] (or, equivalently, [tex]3.2\%[/tex],) assuming that the availabilities of the [tex]12[/tex] jurors are independent from one another.
Step-by-step explanation:
The question states that the probability that a given juror is unavailable is approximately [tex]0.25[/tex].
For the complement of that event, the probability that this particular juror is available would be [tex]1 - 0.25 = 0.75[/tex].
Assume that the availabilities of the [tex]12[/tex] jurors are independent from one another. The number of available jurors would be a binomial variable with [tex]n = 12[/tex] and [tex]p = 0.75[/tex] ([tex]12\![/tex] independent observations, each with a [tex]0.75[/tex] probability of being "available".)
Hence, the probability that all [tex]12[/tex] jurors are available would be:
[tex](0.75)^{12} \times (0.25)^{0} \approx 0.032 = 3.2\%[/tex].
