Select the correct answer. Alexis wants to buy $\$ 500$ worth of new clothes before school starts. She decides to have a garage sale to earn the money for the clothes. She hopes to sell her comic book collection for $\$ 200$, stuffed toys for $\$ 100$, a bicycle for $\$ 50$, and a few knicknacks from her room for $\$ 250$. The probabilities that her neighbors want to buy the stuff Alexis is selling are distributed as shown in the table. \begin{tabular}{|c|c|} \hline$P(X)$ & Probability \\ \hline Comics & $\frac{1}{4}$ \\ \hline Toys & $\frac{1}{4}$ \\ \hline Bikes & $\frac{1}{4}$ \\ \hline Knicknacks & $\frac{1}{4}$ \\ \hline \end{tabular} What is Alexis's expected garage sale income, and how much more would she need to earn to break even? A. The expected income is $\$ 150$, and Alexis would need $\$ 350$ more to break even. B. The expected income is $\$ 600$, and Alexis would need $\$ 100$ less to break even. C. The expected income is $\$ 300$, and Alexis would need $\$ 200$ more to break even. D. The expected income is $\$ 178.50$, and Alexis would need $\$ 321.50$ more to break even. (c) 2023 Edmentum. All rights reserved. Reset Next
Solution
Step 1 ：First, we calculate the expected income from each item. The expected income from an item is the product of the price of the item and the probability that it will be sold.
Step 2 ：The expected income from the comics is \(200 \times \frac{1}{4} = \$50\).
Step 3 ：The expected income from the toys is \(100 \times \frac{1}{4} = \$25\).
Step 4 ：The expected income from the bike is \(50 \times \frac{1}{4} = \$12.50\).
Step 5 ：The expected income from the knicknacks is \(250 \times \frac{1}{4} = \$62.50\).
Step 6 ：Adding these up, the total expected income from the garage sale is \(50 + 25 + 12.50 + 62.50 = \$150\).
Step 7 ：Since Alexis wants to earn \$500, she would need \(500 - 150 = \$350\) more to break even.
Step 8 ：So, the correct answer is A. The expected income is \$150, and Alexis would need \$350 more to break even. \(\boxed{\text{A}}\)
