Question

A sweepstakes offers a first prize of $1,000,000, second prize of $100,000, and third prize of $10,000. Suppose that two million people enter the contest and three names are drawn randomly for the three prizes. Find the expected winnings for a person participating in this contest.

Answer 1

To calculate the expected winnings in the sweepstakes, the value of each prize is multiplied by the probability of winning that prize, resulting in an expected winnings of $0.555 for a person.

Step-by-step explanation:

To find the expected winnings for a person participating in the given sweepstakes, we need to multiply the value of each prize by the probability of winning that prize and then add these values together. With two million people entering and three prizes, the probability of winning the first prize is 1/2,000,000, the second prize is also 1/2,000,000, and the third prize is 1/2,000,000.

The expected winnings (E) for a person can be calculated using the formula:

E = (Value of first prize × Probability of winning first prize) + (Value of second prize × Probability of winning second prize) + (Value of third prize × Probability of winning third prize)

Substituting the given values:

E = ($1,000,000 × 1/2,000,000) + ($100,000 × 1/2,000,000) + ($10,000 × 1/2,000,000)

E = $0.50 + $0.05 + $0.005

E = $0.555

So, the expected winnings for a person is $0.555.