Question

To determine which of two people gets a prize, a coin is flipped twice. If the flips are a Head and
then a Tail, the first player wins. If the flips are a Tail and then a Head, the second player wins.
However, if both coins land the same way, the flips don’t count and whole the process starts over.
Assume that on each flip, a Head comes up with probability p, regardless of what happened on
other flips. Use the four step method to find a simple formula for the probability that the first
player wins. What is the probability that neither player wins?
Suggestions: The tree diagram and sample space are infinite, so you’re not going to finish drawing
the tree. Try drawing only enough to see a pattern. Summing all the winning outcome probabilities directly is difficult. However, a neat trick solves this problem and many others. Let s be the
sum of all winning outcome probabilities in the whole tree. Notice that you can write the sum of all
the winning probabilities in certain subtrees as a function of s. Use this observation to write an equation
in s and then solve.

Answer 1

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