A fair coinis flipped repeatedly. We’ll denote theoutcome of each throw by H or

Question

A fair coinis flipped repeatedly. We’ll denote theoutcome of each throw by H or T (for heads and tails). Find thefollowing probabilities:

(a) Theprobability of getting T on the first throw, Hon the second throw, and H on the third throw.

(b) Theprobability that the third throw gives H.

(c) Theprobability that the first and the thirdthrows give the same outcome.

(d) Theprobability that the first time ofgetting a H is on the 4th throw.

(e) The probability thatthere are at least two Hs during the first 3 throws

Explanation / Answer

a) We need, in order, THH. prob = (1/2)(1/2)(1/2) = 1/8 b) In third throw, it could either be a head or a tail. Thus,prob = 1/2 c) We can either have TT or HH for the first and third throw.In total there are 2x2 = 4 different outcomes for  thefirst and third throw. Therefore, prob = 2/4 = 1/2 d) We need to have TTTH. Thus, prob = (1/2)(1/2)(1/2)(1/2) =1/16 e) It has to be HHH, HHT, HTH or THH. Thus, prob = 4/ 2^3 = 4/8 = 1/2

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