Question

Expected Value for a Magazine Sweepstakes Reader's Digest ran a sweepstakes in which the prizes were listed along with the chances of winning: $1, 000, 000 (1 chance in 80, 000,000), $100, 000 (1 chance in 110, 000, 000), $25,000 ( 1 chance in 110, 000,000), $5000 ( 1 chance in 36, 600, 000), and $2, 500 ( 1 chance in 28, 500, 000) a) Assuming that there is no cost for entering the sweepstakes, find the expected value of the amount won for the one entry b) Find the expected value if the cost of entering this sweepstakes is the cost of a postage stamp- $0.82. Is it worth entering this contest? Note: Make a table with columns for the possible outcomes and the probability of each of the outcomes. Use the table to calculate the expected value in part a. Then use the value from part a to calculate the expected value in part b.

Answer 1

(a) The table showing the prize money and the probabilitites is as below:

Prize Money	Probability	Prize x Probability
1000000	1.25E-08	0.0125
100000	9.09091E-09	0.000909091
25000	9.09091E-09	0.000227273
5000	2.73224E-08	0.000136612
2500	3.50877E-08	8.77193E-05
	SUM	0.013860695

The expected value of the amount won is $ 0.014

(b) If the cost of entry is $ 0.82, the expected money to be won = 0.02-0.82 = -$ 0.80

So the expected loss is $ 0.80. Hence it is not worth entering the contest.