Score: 0 of 4 points
You buy a lottery ticket to a lottery that costs per ticket. There are only 300 tickets available to be sold in this lottery. In this lottery there are one prize(s), two prizes, and fifteen
prizes. Find your expected gain or loss. (Round to 2 decimal places if needed.)
Expected gain or loss Enter your answer
Note: Represent a gain with a positive answer and a loss with a negative answer.

Ask by Macdonald Paul. in the United States

Mar 15,2025

Question

Score: 0 of 4 points
You buy a lottery ticket to a lottery that costs per ticket. There are only 300 tickets available to be sold in this lottery. In this lottery there are one prize(s), two prizes, and fifteen
prizes. Find your expected gain or loss. (Round to 2 decimal places if needed.)
Expected gain or loss Enter your answer
Note: Represent a gain with a positive answer and a loss with a negative answer.

Ask by Macdonald Paul. in the United States

Mar 15,2025

UpStudy AI · Accepted Answer

Let the net outcome be the prize amount minus the cost of the ticket. The cost of the ticket is $$\$15$$.

There are:
- 1 prize of $$\$500$$ with net gain $$\$500 - \$15 = \$485$$,
- 2 prizes of $$\$100$$ with net gain $$\$100 - \$15 = \$85$$,
- 15 prizes of $$\$25$$ with net gain $$\$25 - \$15 = \$10$$,
- The remaining $$300 - 1 - 2 - 15 = 282$$ tickets have no prize and give a net loss of $$\$15$$ (i.e. $$-\$15$$).

The probability of each outcome is:
$$
P(500) = \frac{1}{300}, \quad P(100) = \frac{2}{300}, \quad P(25) = \frac{15}{300}, \quad P(\text{no prize}) = \frac{282}{300}.
$$

The expected gain (or loss) $$E$$ is given by:
$$
E = \frac{1}{300}(485) + \frac{2}{300}(85) + \frac{15}{300}(10) + \frac{282}{300}(-15).
$$

Calculating each term:
$$
\frac{1}{300}(485) = \frac{485}{300} \approx 1.62,
$$
$$
\frac{2}{300}(85) = \frac{170}{300} \approx 0.57,
$$
$$
\frac{15}{300}(10) = \frac{150}{300} = 0.50,
$$
$$
\frac{282}{300}(-15) = -\frac{4230}{300} \approx -14.10.
$$

Now, sum these contributions:
$$
E \approx 1.62 + 0.57 + 0.50 - 14.10 \approx -11.41.
$$

Rounded to two decimal places, your expected gain or loss is approximately $$-\$11.41$$.
Your expected loss is approximately \$11.41.

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