47-50 Expected Value These exercises involve expected value.

Rolling Dice Two dice are rolled. John gets $ 5 if they show the same number; he pays $ 1 if they show different numbers. What is the expected value of this game?

The expected value of the game.

Approach:

The expected value is given as,

E=a1p1+a2p2...(1)

Here, a1 is the amount of winning, a2 is the amount to be paid and p1 and p2 is the probability of payout.

Given:

John wins $5 if two dice are rolled and shows the same number, and he loses $1 otherwise.

Calculation:

The probability of the two dice rolled together and shows the same number is 16 and the probability of the two dice shows two different number is 56.

Calculate the expected value of the game