Question

In arguing against the death penalty, Amnesty International has pointed out supposed inequities, such as the many times a black person has been given the death penalty by an all-white jury. If jurors are selected randomly from an adult population, find the probability that all 12 jurors are white when the population is (a) 90% white and (b) 50% white.

Answer 1

(a) 0.2824

(b) 0.0002441

Explanation:

Assuming that the population is large enough to behave as a binomial distribution (between whites and non-whites), the probability of 12 out of 12 juros being white is:

`P(w=12) = p(w)^(12)`

Where p(w) is the proportion of the population that is white:

(a) for p = 0.90

`P(w=12) = 0.90^(12)\\P(w=12) =0.2824`

The probability is 0.2824.

(b) for p = 0.50

`P(w=12) = 0.50^(12)\\P(w=12) =0.0002441`

The probability is 0.0002441.