One thousand tickets are sold at $1 each. There are four prizes available of: $100, $50, $25 and $10. What is the expected value, if a person purchases two tickets?
To find the expected value, we need to calculate the probability of winning each prize and multiply it by the value of that prize.
There are 1000 tickets sold and 2 tickets purchased, for a total of 2000 possible outcomes (since there are no limitations on the number of tickets a person can win).
The probability of winning the $100 prize is 1/1000, as there is only one $100 prize and 1000 tickets sold.
The expected value for the $100 prize is: (1/1000) * $100 = $0.10.
The probability of winning the $50 prize is also 1/1000.
The expected value for the $50 prize is: (1/1000) * $50 = $0.05.
Similarly, the probabilities for winning the $25 and $10 prizes are both 1/1000.
The expected value for the $25 prize is: (1/1000) * $25 = $0.025.
The expected value for the $10 prize is: (1/1000) * $10 = $0.01.
Adding up these expected values for the four prizes, we get:
$0.10 + $0.05 + $0.025 + $0.01 = $0.185.
Therefore, the expected value of purchasing two tickets is $0.185.