the nfl has determined that out of all drafted college footb

the nfl has determined that out of all drafted college football players, only 60% will actually be qualified to play professional football. to aid in screening out the unqualified draftees, all draftees are put thru physical test that 95% of the qualified draftees will pass, but only 15% of the unqualified draftees will pass. select draftees at random.what is the probability he will pass the test? if he passes the test, what is the probability he is unqualified

Solution

what is the probability he will pass the test?

0.60 * 0.95 + 0.40*0.15

0.63

if he passes the test, what is the probability he is unqualified

P = 0.15 * 0.60   / 0.63

P = 0.1428