Justin writes inane jingles rapidly but poorly. He has a probability of 0.7 of submitting his entry first. If Rustin has not already won the contest, then Justin’s entry will be declared the winner with probability 0.3.
Rustin writes slowly but he has a gift for this sort of thing. If Justin has not already won the contest, by the time of Rustin’s entry, then Rustin will be declared the winner with probability 0.6.
Let the probability that Justin wins the contest be A.
Given that Justin wins, probability that Rustin’s entry arrived first be B.
Probability that the first entry wins the contest be C.
(each of A,B,C -- after rounding off to 3 decimal places)