Question

A magazine ran a sweepstakes in which 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), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000).

a. Assuming that there is no cost to enter the sweepstakes, find the expected value of the amount won for one entry. _____¢. (Round to the nearest tenth as needed.)

b. Find the expected value if the cost of entering this sweepstakes is the cost of a postage stamp (3¢). _____ ¢ (Round to the nearest tenth as needed.)

Is it worth entering this contest?

A. Yes. It is worth entering this contest because the new expected value is negative.

B. No. It is not worth entering this contest because the new expected value is positive.

C. Yes. It is worth entering this contest because the new expected value is positive.

D. No. It is not worth entering this contest because the new expected value is negative.

Answer #1

1.A fair die is rolled once, and the number score is noted.
Let the random variable X be twice this score. Define the variable
Y to be zero if an odd number appears and X otherwise. By finding
the probability mass function in each case, find the expectation of
the following random variables:
Please answer to 3 decimal places.
Part a)X
Part b)Y
Part c)X+Y
Part d)XY
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