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Category > Computer Science Posted 04 May 2017 My Price 5.00

To determine which of two people gets a prize

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 sub trees as a function of s. Use this observation to write an equation in s and then solve.

 

 

Answers

Alpha Geek
(8)
Status NEW Posted 04 May 2017 11:05 AM My Price 5.00

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Attachments

file 1493897455-Answer.docx preview (274 words )
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