Question

Problem 3 At a raffle, there is a grand prize of $200 and five consolation
prizes of $20.
They sell 500 tickets.
At the end of the day, six winning tickets are drawn at random - meaning
that every ticket sold has the same probability of 1/500 to win any one of
the six prizes.
a) What are the expected winnings of this game (the expected value of the
amount one ticket wins)?
b) One ticket costs $3. What is the expected value of one ticket? Please
show work - the answer alone will not get full credit.

Answer 1

We will see that the expected values are:

• a) EV = $0.60
• b) EV = -$2.40

What is the expected value?

For an event with n outcomes {x₁, x₂, ..., xₙ} each one with probability {p₁, p₂, ..., pₙ}, the expected value is:

$EV = \sum x_i*p_i$

So here we have 3 outcomes:

• Winning $200, with a probability of 1/500.
• Winning $20, with a probability of 5/500.
• Winning nothing, with a probability of 494/500.

a) So the expected value is:

EV = $200/500 + $20*(5/500) + $0*(494/500)  = $0.60

b) If one ticket costs $3, to get the new expected value we just need to subtract $3 to the one we got above because you are paying $3 to get the ticket.

EV = $0.60 - $3 = -$2.40

So in this case we have a negative expected value.

If you want to learn more about expected value, you can read:

https://brainly.com/question/15858152