20.03.2023 - 08:47

Reader’s 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 (1 chance in 110,0

Reader’s 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 (1 chance in 110,000,000), $5,000 (1 chance in 36,367,000), 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 sweepstake is the cost of a postage stamp – $0.89. Is it worth entering this contest?

Answers (1)
  • bormanchik
    April 5, 2023 в 03:20

    a) The expected value of the amount won for one entry is the sum of the products of the probability of winning each prize and the value of each prize. Mathematically, it can be expressed as:

    Expected value = (1/90,000,000) * $1,000,000 + (1/110,000,000) * $100,000 + (1/110,000,000) * $25,000 + (1/36,367,000) * $5,000 + (1/27,500,000) * $2,500

    Expected value = $0.011111...

    Therefore, the expected value of the amount won for one entry is \approx imately $0.0111.

    b) If the cost of entering the sweepstakes is $0.89, we need to subtract this cost from the expected value calculated above to determine if it is worth entering the contest.

    Expected value after deducting the cost of entry = $0.011111... - $0.89 = -$0.8789

    The expected value after deducting the cost of entry is negative, which means that on average, we can expect to lose money by entering the contest. Therefore, it is not worth entering the contest if the cost of entry is $0.89.

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