Question

A lottery offers one $900 prize, two $600 prizes, two $300 prizes, and five $200 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys five tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize, Round to two decimal places for currency problems.

The expectation if a person buys five tickets is ___ dollar(s).

Answer 1

The expectation if a person buys five tickets is $-2.10.

Step-by-step explanation:

The expectation if a person buys five tickets is $-2.10.

To calculate the expected value, we need to multiply the probability of winning each prize by the amount of the prize.

1. The probability of winning the $900 prize is 1/1000. Multiply this by $900.
2. The probability of winning one of the two $600 prizes is 2/1000. Multiply this by $600.
3. The probability of winning one of the two $300 prizes is 2/1000. Multiply this by $300.
4. The probability of winning one of the five $200 prizes is 5/1000. Multiply this by $200.

Summing up all the products gives us the expected value, which is -$2.10.