Question

The City College football team consists of seven freshmen, eight sophomores, sixjuniors, and nine seniors. Four of them will be selected at random and given a drug test. Giventhat none of the selected players are seniors, what is probability that at most two freshmen areselected for the test?

Answer 1

0.9123 or 91.23%

Explanation:

Given that none of the selected players are seniors, there are 7 freshmen, 8 sophomore and 6 juniors left (total of 21 players). Since four players are selected, the probability that at most two freshmen are selected is 100% minus the probability that either 4 or 3 freshmen are selected:

`P(X\leq 2)=1-P(X=4)-P(X=3)\\P(X\leq 2)=1-(7)/(21)*(6)/(20)*(5)/(19)*(4)/(18)-4*(7)/(21)*(6)/(20)*(5)/(19)*(14)/(18)\\P(X\leq 2)=0.9123=91.23\%`

The probability is 0.9123 or 91.23%