Question

HW Score: 69.7%, 7.67 of 11 points Homework: Ch 8.5 - Random V... Question 8, 8.5.39 Save O Points: 0 of 1 Question Viewer Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $800, 3 prizes of $100, 5 prizes of $10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket? Let X be the random variable for the amount won on a single raffle ticket. EX)=dollars (Round to the nearest cent as needed.)

Answer 1

To calculate the expected value (E[X]) for the amount won on a single raffle ticket, you need to multiply each possible prize amount by its respective probability of winning and then sum these values.

Here are the prizes and their probabilities:

- 1 prize of $800 with a probability of 1/5000 (1 winner out of 5000 tickets).

- 3 prizes of $100 each with a probability of 3/5000 (3 winners out of 5000 tickets).

- 5 prizes of $10 each with a probability of 5/5000 (5 winners out of 5000 tickets).

- 20 prizes of $5 each with a probability of 20/5000 (20 winners out of 5000 tickets).

Now, calculate the expected value:

E[X] = (1/5000) * $800 + (3/5000) * $100 + (5/5000) * $10 + (20/5000) * $5

E[X] = $0.16 + $0.06 + $0.01 + $0.02

E[X] = $0.25

So, the expected value of this raffle if you buy 1 ticket is $0.25 (rounded to the nearest cent).