Question

A mogazine ran a sweepstakes in which prizes were lisbed along whth the chances of winning: $1,000,000 (1 chance in 60,000,000). $100,000 (1 chanco in 120,000,000). $25,000 (1 chance in 120,000,000)$5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000 ) Complete a and b a. Assuming that there is no cost to enter the ewneptakes, find the expected valos of the amount won for one entry. (Round to the nearest teren as needed.)

Answer 1

To find the expected value of the amount won for one entry in the sweepstakes, multiply each prize amount by its probability and add the products together, yielding approximately $0.018 per entry.

Step-by-step explanation:

The expected value of the amount won for one entry in the magazine sweepstakes can be calculated by multiplying the prize value by the probability of winning that prize and summing these products for all the prizes. To find the probability, take the reciprocal of the chances. Then, multiply each prize by its probability and add these numbers together:

• Expected value for $1,000,000 prize = $1,000,000 × (1 / 60,000,000) = $0.01667
• Expected value for $100,000 prize = $100,000 × (1 / 120,000,000) = $0.00083
• Expected value for $25,000 prize = $25,000 × (1 / 120,000,000) = $0.00021
• Expected value for $5,000 prize = $5,000 × (1 / 36,667,000) = $0.00014
• Expected value for $2,500 prize = $2,500 × (1 / 27,500,000) = $0.00009

Summing them up gives the total expected value: $0.01667 + $0.00083 + $0.00021 + $0.00014 + $0.00009 = $0.01804 per entry, rounding to the nearest cent as needed.