A coin is biased so that a head is twice as likely to occur as a tail. This coin

Question

A coin is biased so that a head is twice as likely to occur as a tail. This coin is tossed by three people in a two-step gambling game. In step 1, the person whose toss is not a match to either of the other two people is the "odd man out." Only the remaining two players whose coin match go on to step 2 to resolve the ultimate winner. What is the probability that a player will advance to step 2 after the first toss? What is the probability that a player will be out after the first toss? What is the probability that no player will we out after the first toss?

Explanation / Answer

P(head) = 2/3

p(tail) = 1/3

P(3 heads) = (2/3)x(2/3)x(2/3) = 0.2963

P(3 tails) = (1/3)(1/3)(1/3) = 0.0370

A)P(a player will advance to step 2 after first toss) = 1 - 0.2963 - 0.0370

= 0.6667

B) P(a player will be out after first toss) = 0.6667

C) P(no player will be out after first toss) = 0.2963 + 0.0370 = 0.3333

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