Question

A and B throw alternately a pair of dice. A wins if he throws 6 before B throws 7 and B wins if she throws 7 before A throws 6. If A begins, his chance of winning would be

Answer 1

Correct answer is A) 30/61

Answer 2

Thank you for asking this question:

Here is your answer:

We know that the probability of A throwing ‘6’ = 5/36 .

The probability of A not throwing would be ‘6’ = 1 – 5/36 = 31/36 .

The probability of B throwing would be ‘7’ = 6/36 .

The probability of B not throwing would be ‘7’ = 1 – 6/36 = 30/36 .

The probability of somebody winning would be =[1-{(31/36)(30/36)}].

So, The probability of winning of A provided that somebody wins would be =

(5/36) / [1-{(31/36) (30/36)}] = 30/61

So 30/61 is the answer.