Question

you buy a lottery ticket to a lottery that costs $10 per ticket. there are only 100 tickets available to be sold in this lottery. in this lottery there are one $700 prize, two $100 prizes, and four $25 prizes. find your expected gain or loss.

Explanation:

Step1: Calculate the probability of each outcome

• The probability of winning the $700$ prize: $P(X = 700-10)=\frac{1}{100}$ (since there is 1 such prize out of 100 tickets)
• The probability of winning a $100$ prize: $P(X = 100 - 10)=\frac{2}{100}$ (2 prizes)
• The probability of winning a $25$ prize: $P(X = 25 - 10)=\frac{4}{100}$ (4 prizes)
• The probability of losing (not winning any prize): $P(X=- 10)=\frac{100-(1 + 2+4)}{100}=\frac{93}{100}$

Step2: Use the expected - value formula

The expected - value formula is $E(X)=\sum_{i}x_{i}P(x_{i})$

$$
LATEXBLOCK0
$$

Answer:

$0$