question 4
4 pts
juanita pays $10 to purchase one raffle ticket in the hopes of winning a new car valued at $27,982. there are 5,608 tickets sold. using the expected value of a ticket, calculate the expected gain or loss to juanita.
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 expected value indicates an expected loss for juanita.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the probability of winning
The probability $ P(\text{win})=\frac{1}{5608}$ and the probability $ P(\text{lose})=\frac{5607}{5608}$

## Step2: Calculate the net gain if win and if lose
If win: Net gain $=27982 - 10=27972$
If lose: Net gain $=- 10$

## Step3: Use the expected - value formula $E(X)=\sum_{i}x_{i}P(x_{i})$
$$
\begin{align*}
E(X)&=(27972)\times\frac{1}{5608}+(-10)\times\frac{5607}{5608}\
&=\frac{27972 - 56070}{5608}\
&=\frac{-28098}{5608}\
&\approx - 5.01
\end{align*}
$$

# Answer:
$-5.01$

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Question

Explanation:

Step1: Calculate the probability of winning

Step2: Calculate the net gain if win and if lose

Step3: Use the expected - value formula \(E(X)=\sum_{i}x_{i}P(x_{i})\)

Answer: