Readers Digest ran a sweepstakes in which the prizes were listed along with the

Question

Readers Digest ran a sweepstakes in which the 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 n (1 chance in 110,000,000), $5000 (1 chance in 36, 667,000), and $2, 500(1 chance in 27, 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 - $0.89. Is it worth entering this contest?

Explanation / Answer

Expected value E(x) =x.P(x)

X

P(x)

x. P(x)

1,000,000

0.0000000111

0.0111

100,000

0.0000000091

0.00091

25,000

0.0000000091

0.000228

5,000

0.0000000273

0.000137

2,500

0.0000000364

0.000091

0.012465

expected value =0.012465 =$1.25

b)

Expected price =1.25 -0.89 =$0.37

X

P(x)

x. P(x)

1,000,000

0.0000000111

0.0111

100,000

0.0000000091

0.00091

25,000

0.0000000091

0.000228

5,000

0.0000000273

0.000137

2,500

0.0000000364

0.000091

0.012465

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