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Proof of density function

In the game of odd man wins, three people toss coins. The game continues until someone has an outcome different from the other two. The individual with the different outcome wins. Let X equal the number of games needed before a decision is reached. Prove by induction that the density function of X is (see attached).

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Proof:

Suppose T is tail, H is head. For one game, there are 8 outcomes:
TTT, HHH, TTH, THT, HTT, HHT, HTH, THH
Two of ...

Solution Summary

This is a probability proof by induction regarding density function.

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