In this problem, we are going to determine the probability of getting strings of

Question

In this problem, we are going to determine the probability of getting strings of consecutive heads when flipping a fair coin. Although the method can be applied more generally, we shall focus on finding the probability of getting at least three consecutive heads in ten flips. We do this recursively, which means that we are going to find an answer by starting with simple cases and showing how to use those to build more complicated ones. We start by finding the number of ways that you can fail to get three consecutive heads in four flips.

A.) How many ways are there to get no more than two consecutive heads in one flip? In two? In three?

Explanation / Answer

In one flip you cannot get two concecutive heads in one flip.

In two flips you can get two concecutive heads in 2C2 = 1 way.

In three flips you can get three concecutive heads in 3C2 = 3 ways.

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