   Chapter 14.CR, Problem 48E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 47-50 Expected Value These exercises involve expected value.Rolling Dice Three dice are rolled. John gets $5 if they all show the same number; he pays$ 1 otherwise. What is the expected value of this game?

To determine

The expected value of the game.

Explanation

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 p1andp2 is the probability of payout.

Given:

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

Calculation:

The total number of outcomes when three dice are rolled together are 216.

Number of outcomes when all three dice shows the same number are 6.

Therefore, the probability of the three dice rolled together and shows the same number is 136 and the probability of the three dice shows three different number is 3536.

Calculate the expected value of the game

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