One thousand raffle tickets are sold for $1.00 each. One grand prize of $400 and two consolation prizes of $100 each will be awarded. Jeremy purchases one ticket. Find his expected value.

??

Think of what you'll get if you bought all the tickets, and go from there.

1,000-600=400 ??

If you bought all 1000 tickets, it would have cost you $1000.

However, you would get the grand prize of $400 and 2 consolation prizes of $100 each for a total of $600.
So you get back $600 for the $1000 that you spent, or, on the average, $0.60 for each ticket you buy.

so his expected value is $600?

What is Jeremy's expected value?

$600? or $400??

But Jen, in the end he only bought one ticket, not 1000. 600/1000

MathMate already told you the answer.

Perhaps it is easier from the point of view of the seller.

Sold 1000 tickets for 1000 dollars.
Gave out 600.
So .6 of the income is paid out. So if you put in $1, you can expect .6 * $1 = $0.60

To find Jeremy's expected value, we need to calculate the probability of winning each prize and the amount of money he would receive for each prize. Let's break it down step by step:

1. Probability of winning the grand prize:
Out of the 1000 raffle tickets sold, only one will win the grand prize. Therefore, the probability of Jeremy winning the grand prize is 1/1000.

2. Amount of money won for the grand prize:
Jeremy will receive $400 if he wins the grand prize.

3. Probability of winning a consolation prize:
There are two consolation prizes, so the probability of Jeremy winning a consolation prize is 2/1000, or 1/500.

4. Amount of money won for a consolation prize:
Jeremy will receive $100 if he wins a consolation prize.

Now we can calculate Jeremy's expected value:

Expected value = (Probability of winning grand prize * Amount won for grand prize) +
(Probability of winning consolation prize * Amount won for consolation prize)

Expected value = (1/1000 * $400) + (1/500 * $100)
Expected value = $0.40 + $0.20
Expected value = $0.60

Therefore, Jeremy's expected value for his one raffle ticket is $0.60.