One thousand raffle tickets are sold for $4.00 each. One grand prize of $800 and two consolation prizes of $100 each will be awarded. Jeremy purchases one ticket. Find his expected value.
Jeremy has a 1/1000 chance at $800 and a 1/500 chance at $100.
800/1000 + 2*100/1000 = $1 is the ticket's expected value, no matter what was paid.
oooooh okay....thank you for your help :)
To find Jeremy's expected value, we need to calculate the average amount of money he can expect to win or lose.
First, let's determine the probability of winning each prize:
- Grand prize of $800: There is only one grand prize, so Jeremy has a 1 in 1000 chance of winning it.
- Consolation prizes of $100 each: There are two consolation prizes, so Jeremy has a 2 in 1000 chance of winning one.
Next, we calculate the value of each prize:
- Grand prize of $800: The value of winning the grand prize is $800.
- Consolation prizes of $100 each: The value of winning a consolation prize is $100.
Now, we can calculate Jeremy's expected value:
Expected value = (Probability of winning grand prize × Value of grand prize) + (Probability of winning consolation prize × Value of consolation prize)
Expected value = (1/1000 × $800) + (2/1000 × $100)
Expected value = ($0.80) + ($0.20)
Expected value = $1.00
Therefore, Jeremy's expected value is $1.00.