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Finding the expected value of a game

On three rolls of a single die you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game?

Solution Preview

First we should calculate the probability that you roll a die 3 times and no 5 comes up. Each toss of the die has a probability of 5/6 of NOT being a 5. So,

P(3 rolls and no 5) = (5/6)^3 = .5787.

This immediately tells us the probability that we will roll at least one 5, out of three rolls. It is simply the following

P(3 rolls and at least one 5) ...

Solution Summary

A step-by-step solution is provided which covers the process of finding the expected value of a game.