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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

APPLICATIONS

Sweepstakes A sweepstakes offers a first prize of $ 1 , 000 , 000 , second prize of $ 100 , 000 , and third prize of $ 10 , 000 . Suppose that two million people enter the contest and three names are drawn randomly for the three prizes.

(a) Find the expected winnings for a person participating in this contest.

(b) Is it worth paying a dollar to enter this sweepstakes?

To determine

(a)

The expected value for a person participating in the contest.

Explanation

Approach:

The expected value is given as,

E=a1p1+a2p2++anpn(1)

Here, a1,a2,,an is the amount of payout and p1,p2,,pn is the probability of payout.

Given:

A sweepstakes offers a first prize of $1,000,000, second prize of $100,000, and third prize of $10,000, and two million people enter in the contest.

Calculation:

The total outcome is 2,000,000. Since the probability of winning the first prize is 12,000,000, the probability of winning the second prize is 12,000,000, and the probability of winning the third prize is 12,000,000.

Calculate the expected value of the game

To determine

(b)

Whether it is worth paying a dollar to enter the sweepstakes.

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Chapter 14 Solutions

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