Question

question 2
4 pts
allison purchases one lottery raffle ticket for a school fundraiser. the raffle ticket cost $16. the school is selling 61,631 tickets. one ticket will be randomly drawn and the winner will receive $20,152. assuming all of the tickets are sold, and using the expected value of a ticket, compute the expected gain or loss for allison.
note: please avoid rounding numbers in the middle of your calculations. however, round your final answer to two decimal places, before entering it in the box below. a negative final answer indicates an expected loss to allison for playing the lottery raffle.

Explanation:

Step1: Calculate the probability of winning and losing

The probability of winning \( P(W)=\frac{1}{61631}\), and the probability of losing \( P(L)=\frac{61630}{61631}\).
The amount won if winning is \( A_W = 20152 - 16=20136\) (subtracting the cost of the ticket), and the amount lost if losing is \( A_L=- 16\).

Step2: Use the expected - value formula

The expected - value formula is \(E = P(W)\times A_W+P(L)\times A_L\).
Substitute the values:

$$
LATEXBLOCK0
$$

Answer:

\(-15.67\)