47-50 Expected Value These exercises involve expected value.
Rolling Dice Three dice are rolled. John gets if they all show the same number; he pays otherwise. What is the expected value of this game?
The expected value of the game.
The expected value is given as,
Here, is the amount of winning, is the amount to be paid and is the probability of payout.
John wins if three dice are rolled and shows the same number, and he loses otherwise.
The total number of outcomes when three dice are rolled together are .
Number of outcomes when all three dice shows the same number are .
Therefore, the probability of the three dice rolled together and shows the same number is and the probability of the three dice shows three different number is .
Calculate the expected value of the game
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