Bo and Ci are the only two people who will enter the Rover Dog Food jingle contest. Only one entry is allowed per contestant, and the judge (Rover) will declare the one winner as soon as he receives a suitably inane entry, which may be never. Bo writes inane jingles rapidly but poorly. He has probability 0. 7 of submitting his entry first. If Ci has not already won the contest, Bo's entry will be declared the winner with probability 0.3. Ci writes slowly, but he has a gift for this sort of thing. If Bo has not already won the contest by the time of Ci's entry, Ci will be declared the winner with probability 0.6. a. What is the probability that the prize never will be awarded?
b. What is the probability that Bo will win?
c. Given that Bo wins, what is the probability that Ci's entry arrived first?
d. What is the probability that the first entry wins the contest?
e. Suppose that the probability that Bo's entry arrived first were P instead of 0.7, Can you find a value of P for which "First entry wins" and "Second entry does not win" are independent events?