A western city has 19 police officers eligible for promotion

A western city has 19 police officers eligible for promotion. Eleven of the 19 are Hispanic. Suppose only five of the police officers are chosen for promotion and that one is Hispanic. If the officers chosen for promotion had been selected by chance alone, what is the probability that one or fewer of the five promoted officers would have been Hispanic? What might this result indicate?It is fairly (unlikely/likely) that these results occur by chance. A researcher (might not want/might want) to further investigate this result to determine causes.

Solution

P = 11/19 = 0.58

n = 5

P( x <= 1 ) = P(x=0) + P(x=1)

P(x=0) = 5C0 * 0.58^0 * 0.42^(5-0) = 0.0131

P(x=1) = 5C1 * 0.58^1 * 0.42^(5-1) = 0.0902

P(x <= 1) = 0.1033

it is fairyl unlikely that these results occur by change , because the probability is very low