Reader’s Digest ran a sweepstakes in which the prizes were listed along with the

Question

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).

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

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.

Explanation / Answer

the expected value of the amount won for the one entry. = 0.014650169

expected value if the cost of entering this sweepstakes is the cost of a postage stamp – $0.82

= 0.014650169 - 0.82

= -0.805349

since E(X) < 0 , it is not worth entering

x p xp 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-07 0.000877193 E(X) 0.014650169

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