A company sends an entry form for a sweepstakes to a lot of people. The prizes f

ID: 3129148 • Letter: A

Question

A company sends an entry form for a sweepstakes to a lot of people. The prizes for the contest are

• One first place award of $10,000,000.

• Two second-place awards of $1,000,000.

• Three third-place awards of $10,000.

• Four fourth-place awards of $1,000.

A person must spend $0.75 to enter the sweepstakes, of which $0.30 goes to the company to offset the prize money, and the other $0.45 is postage.

• How many entries are required in order to offset the total amount of the prize money?

• Assuming exactly that many entries are received, what is the expected gain or loss for a single entry?

Let number of entries required be n.

Amount spent in prizes = 1*10,000,000 + 2*1,000,000 + 3*10,000 + 4*1,000 = 12034000

Amount to offset prize = 0.30*n

So, 0.30*n = 12034000

n = 40,113,333.333

or entries required = 40,113,334 (rounded off)

For a single entry,

P(1st prize) = 1/40,113,334

P(2nd prize) = 2/40,113,334

P(3rd prize) = 3/40,113,334

P(4th prize) = 4/40,113,334

E[Loss] = 1/40,113,334*10,000,000 + 2/40,113,334*1,000,000 + 3/40,113,334*10,000 + 4/40,113,334*1,000 - 0.30

= 0

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