# Probability of making your 3rd shot on or by the 5th attempt

Suppose that the probability of making a three pointer is p=35%.

a) Calculate the probability that you make your third shot ON your fifth attempt.

b) Calculate the probability that you make your third shot BY your fifth attempt.

I got a, but can't figure out how to solve b: the book says the answer to be is .2352.

• Calculate the probability that you make your third shot on your third attempt. Calculate the probability that you make your third shot on your fourth attempt. Calculate the probability that you make your third shot on your fifth attempt. Add up the mutually exclusive probabilities Apr 4, 2014 at 21:49

You make your third shot on your third attempt with the probability of: $0.35^3$.
You make your third shot on your fourth attempt with the probability of: $\binom{3}{2}\cdot0.65\cdot0.35^3$
You make your third shot on your fifth attempt with the probability of: $\binom{4}{2}\cdot0.65^2\cdot0.35^3$