Problem 9RE

Expected Value for a Magazine Sweepstakes Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000).

a. Assuming that there is no cost of entering the sweepstakes, find the expected value of the amount won for one entry.

b. Find the expected value if the cost of entering this sweepstakes is the cost of a postage stamp. Is it worth entering this contest?

Answer:

Step 1:

Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000).

a). To find the expected value of the amount won for one entry.

The expected value of the amount won for one entry is

=

Therefore the expected price value is 0.012.

b). The expected value will be 0.012 minus the cost of the postage stamp. Because the expected value of winning is much smaller than the cost of a postage stamp,it is not worth entering the contest.