Question

use the following statement to answer parts a) and b). one hundred raffle tickets are sold for $3 each. one prize of $200 is to be awarded. winners do not have their ticket costs of $3 refunded to them. raul purchases one ticket.
a) determine his expected value.
b) determine the fair price of a ticket.
a) his expected value is $ (type an integer or a decimal.)

Explanation:

Step1: Calculate the probability of winning and losing

• There are 100 tickets. The probability of winning \( P(W)=\frac{1}{100} = 0.01\)
• The probability of losing \( P(L)=\frac{99}{100}=0.99\)

Step2: Calculate the net - gain for winning and losing

• If Raul wins: The prize is $200, but he paid $3 for the ticket. So the net - gain \(x_1=200 - 3=197\)
• If Raul loses: The net - gain \(x_2=- 3\)

Step3: Use the expected - value formula \(E(X)=\sum_{i = 1}^{n}x_ip_i\)

$$
LATEXBLOCK0
$$

Answer:

-1