AandB rolladie.Awinsifthedieshowsa6andB winsifthedieshowsa1. The die is rolled u

Question

AandB rolladie.Awinsifthedieshowsa6andB winsifthedieshowsa1. The die is rolled until someone wins. What is the probability that A wins? What is the probability that B wins? Let T be the number of times the die is rolled. Find the distribution of T .
AandB rolladie.Awinsifthedieshowsa6andB winsifthedieshowsa1. The die is rolled until someone wins. What is the probability that A wins? What is the probability that B wins? Let T be the number of times the die is rolled. Find the distribution of T .
AandB rolladie.Awinsifthedieshowsa6andB winsifthedieshowsa1. The die is rolled until someone wins. What is the probability that A wins? What is the probability that B wins? Let T be the number of times the die is rolled. Find the distribution of T .

Explanation / Answer

P(dice having 6) = 1/6

P(dice having 1) = 1/6

P( A winning) = 1/6 +4/6*1/6+ 4/6*4/6*1/6 ......

It's a gp with r = 4/6

Thus, sum = a/(1-r) = 1/2

Thus probability of a winning is 0.5

Similarly, probability of b winning = 0.5

P(T=1) = 1/6 + 1/6 = 1/3

P(T=2) = 2*4/6*1/6 = 8/36

P(T= k) = (4/6)^{k-1} * 2/6

It is a geometric distribution

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