Three contestants in a quiz show have to answer, in turn, a series of questions. Let p1, p2, and p3 be the probabilities that the first, second, and third player answer a question correctly. The game ends when the first correct answer is given. For n = 1, 2,…, define the events An∶ the first player wins the game at the nth round of questions.

(a) Show that

b) Find the probability that the first player wins the game;

(c) By finding the winning probabilities of the other two players, examine whether it is possible that the game goes on forever.

Transcribed Image Text:

P(A)= [(1-P)(1-P2)(1 - P3)]"P