Lottery Prizes A lottery offers one prize, two prizes, three prizes, and five prizes. One thousand tickets are sold at 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).
To find the expectation, we need to calculate the expected value for each prize and then sum them up.
Let's consider each prize separately:
- One prize: There is a $1,000 prize and 4 tickets are purchased. Each ticket has a 1/1000 probability of winning this prize. So, the expected value for this prize is 1/1000 * $1,000 = $1.
- Two prizes: There is a $500 prize and 4 tickets are purchased. Each ticket has a 1/500 probability of winning this prize. So, the expected value for this prize is 1/500 * $500 = $1.
- Three prizes: There is a $250 prize and 4 tickets are purchased. Each ticket has a 1/250 probability of winning this prize. So, the expected value for this prize is 1/250 * $250 = $1.
- Five prizes: There is a $100 prize and 4 tickets are purchased. Each ticket has a 1/100 probability of winning this prize. So, the expected value for this prize is 1/100 * $100 = $1.
Now, let's sum up the expected values for each prize:
$1 + $1 + $1 + $1 = $4
Therefore, the expected value if a person buys four tickets is $4.