Question

question 2
4 pts
allison purchases one lottery raffle ticket for a school fundraiser. the raffle ticket cost $10. the school is selling 39,236 tickets. one ticket will be randomly drawn and the winner will receive $37,656. 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 \( P(W)=\frac{1}{39236} \), and the probability of losing \( P(L)=\frac{39235}{39236} \).
The amount won if winning is \( 37656 - 10=37646 \) (subtracting the cost of the ticket), and the amount lost if losing is \( - 10 \).

Step2: Use the expected - value formula

The expected - value formula is \( E(X)=\sum_{i}x_{i}P(x_{i}) \).
Here, \( E(X)=(37646)\times\frac{1}{39236}+(- 10)\times\frac{39235}{39236} \).

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LATEXBLOCK0
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Answer:

\(-9.04\)