Question

Lottery Prizes A lottery offers one $1000 prize, two $500 prizes, three $300 prizes, and four $200 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys four 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 four tickets is dollar(s),

Answer 1

To find the expectation if a person buys four tickets in the lottery, calculate the expected value by multiplying the probability of winning each prize by the value of that prize and then adding up the results. The expectation if a person buys four tickets is $14.80.

Step-by-step explanation:

To find the expectation if a person buys four tickets in the lottery, we need to calculate the expected value by multiplying the probability of winning each prize by the value of that prize and then adding up the results.

1. Probability of winning the $1000 prize = 1/1000 * 4 (since four tickets are bought) = 0.004
2. Probability of winning the $500 prize = 2/1000 * 4 = 0.008
3. Probability of winning the $300 prize = 3/1000 * 4 = 0.012
4. Probability of winning the $200 prize = 4/1000 * 4 = 0.016

Expected value = (0.004 * $1000) + (0.008 * $500) + (0.012 * $300) + (0.016 * $200) = $4 + $4 + $3.6 + $3.2 = $14.80

Therefore, the expectation if a person buys four tickets is $14.80.

Answer 2

The expectation if a person buys four tickets is $5.20.

Step-by-step explanation:

To find the expectation if a person buys four tickets, we need to calculate the expected value of the winnings.

The probability of winning each prize is as follows:

$1000 prize = 1/1000,

$500 prize = 2/1000,

$300 prize = 3/1000, and

$200 prize = 4/1000.

The expected value is calculated by multiplying the probability of winning each prize by the value of that prize, and then summing all of these values.

For example: (1/1000) * $1000 + (2/1000) * $500 + (3/1000) * $300 + (4/1000) * $200 = $5.20

So, the expectation if a person buys four tickets is $5.20.