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I am having some problems solving this exercise. Can somebody give a hint on how to solve this. The hint from the book is not really helping me.

1. The problem statement, all variables and given/known data

Two sharpshooters, A and B, are going to shoot at a target. A has probability Pa of hitting it on a single shot; B has probability Pb of hitting it on a single shot. Wheater the target is struck on any one shot is statistically independent of whether it is struck on any other shot. What is the probability that B needs to shoot more times before hitting the target than A?

(Hint from the book:

1. Suppose that A hits the target for the first time on his nth shot.

2. Calculate the probabity that B shoots more than n times before hitting the target

3. Then use the principle of total probabity to account for all values of n from 1 ad infinium)

2. Relevant equations

Pr(M AND M) = Pr(M|Ai)*Pr(Ai)

Pr(M) = Pr(M|A1)*Pr(A1) + Pr(M|A2)*Pr(A2) ...

3. The attempt at a solution

P(A nth shot) = Pa*(1-Pa)^(n-1)

P(B nth+1 shot) = Pb*(1-Pb)^n

????

Thank you

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# Homework Help: Probability: B needs to shoot more times than A

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