DISCUSS DISCOVER PROVE WRITE

DISCUSS: The Expected Value of a Sweepstakes Contest

A magazine clearinghouse holds a sweepstakes contest to sell subscriptions. If you return the winning number, you win $ 1 , 000 , 000 . You have a 1-in-20-million chance of winning, but your only cost to enter the contest is a first-class stamp to mail the entry. Use the current price of a first-class stamp to calculate your expected net winnings if you enter this contest. Is it worth entering the contest?

To find:

Whether it is worth entering the contest.

Approach:

Fair game is game with expected value zero, if you are play a fair game many times, you would expect, on average, to break even.

To check whether the games is fair or not first calculate the expected value of event by using following formula.

E=a1p1+a2p2+...appn

Here, E is expected value, a1, a2, and an are game payouts, and p1, p2, and pn is probabilities.

Calculation:

Given that, there are 1 in 20 million chance of winning $1,000,000. So, the probability of winning is 120,000,000. Use $0.45 stamp to send in the numbers.

The probability of loose is,

p2=1−120,000,000=19,999,99920,