Two dice are rolled. John gets $5 if they show the same number, or he pays $1 if they show different numbers. What is the expected value of this game?
There are six out of 36 possible outcomes to show the numbers (1,1),(2,2),(3,3),(4,4),(5,5) and (6,6). The probability that two dice show the same number is 636=16. Thus, the probability that the two dice show two different numbers is 1−16=56. Thus, the expected value of this game is
5(16)−1(56)=0
In other words, if you play this game many times, you would accept to earn nothing on every dollar you bet on average.
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