suppose a local symphony decides to raise money by raffling a microwave oven worth $400, a diner for two worth $80, and 2 books worth $20 each. a total of 2000 tickets are sold at $1 each. find the expected value of wining for a person who buys one ticket in the raffle.
expected value = (400 + 80 + 40)(1/2000) = .26
so the expected value of winning is 26 cents
To find the expected value of winning for a person who buys one ticket in the raffle, we need to calculate the probability of winning and the corresponding value of the prize.
First, let's determine the probability of winning each individual prize.
The microwave oven has a value of $400, and there is only one available. Since a total of 2000 tickets are sold, the probability of winning the microwave oven is:
P(microwave oven) = 1 / 2000
The diner for two is worth $80, and there is only one available. Therefore, the probability of winning the diner for two is:
P(diner for two) = 1 / 2000
There are 2 books available, each worth $20. So, the probability of winning a book is:
P(book) = 2 / 2000 = 1 / 1000
Now, let's calculate the expected value of winning for each individual prize.
Expected value of winning the microwave oven = P(microwave oven) * value of microwave oven
Expected value of winning the diner for two = P(diner for two) * value of diner for two
Expected value of winning a book = P(book) * value of a book
For the microwave oven:
Expected value of winning the microwave oven = (1 / 2000) * $400 = $0.20
For the diner for two:
Expected value of winning the diner for two = (1 / 2000) * $80 = $0.04
For each book:
Expected value of winning a book = (1 / 1000) * $20 = $0.02
Now, let's find the total expected value of winning for a person who buys one ticket in the raffle by adding up the expected values of winning each prize:
Expected value of winning = Expected value of winning the microwave oven + Expected value of winning the diner for two + Expected value of winning a book
Expected value of winning = $0.20 + $0.04 + $0.02 = $0.26
Therefore, the expected value of winning for a person who buys one ticket in the raffle is $0.26.