My Courses CRN 40938 Chapter 4 HW - Discrete Random Variable Current score: *A!, Category: Homework 36/100 points Submit assignment A theater group holds a fund-raiser. It sells 100 raffle tickets for $$ \$ 6 $$ apiece. There is only 1 winning ticket in 100 raffle tickets. Suppose you purchase five tickets. The prize is two passes to a Broadway show, worth a total of $$ \$ 170 $$. a. As a statistics student who wants to win money playing the game, what should you be interested in? A The prize B The expected value of profit C The number of tickets D The price of each ticket b. Which of the following defines the random variable $$ X $$ ? A The net profit earned by purchasing five tickets. B The total purchase price of five tickets C The number of raffle tickets purchased D None of the above c. List the values that $$ X $$ may take on. (Separate the values with commas.) $$ x= $$ Enter your answer

Question

UpStudy AI · Accepted Answer

Sure, let's work through each part of your homework problem step by step.

---

### **Problem Overview**
A theater group is holding a fundraiser by selling 100 raffle tickets at \$6 each. Only 1 ticket will win, and the prize is two passes to a Broadway show worth \$170 total. You decide to purchase five tickets.

---

### **Part a**

**Question:**
_As a statistics student who wants to win money playing the game, what should you be interested in?_

**Options:**
- **A** The prize
- **B** The expected value of profit
- **C** The number of tickets
- **D** The price of each ticket

**Answer: B. The expected value of profit**

**Explanation:**
As a statistics student aiming to evaluate the profitability of the raffle, you're most interested in the **expected value of profit**. This involves calculating the average outcome you can expect over many trials, considering both the cost of tickets and the potential winnings. Understanding the expected value helps in making informed decisions about whether participating in the raffle is financially beneficial in the long run.

---

### **Part b**

**Question:**
_Which of the following defines the random variable $$ X $$?_

**Options:**
- **A** The net profit earned by purchasing five tickets.
- **B** The total purchase price of five tickets
- **C** The number of raffle tickets purchased
- **D** None of the above

**Answer: A. The net profit earned by purchasing five tickets.**

**Explanation:**
A **random variable** $$ X $$ represents a numerical outcome of a random event. In this context:
- **Option A** correctly identifies $$ X $$ as the **net profit**, which varies depending on whether you win or lose.
- **Option B** is a fixed cost and does not vary.
- **Option C** is a constant value (five tickets) and does not vary.

Thus, **Option A** is the correct definition of the random variable $$ X $$.

---

### **Part c**

**Question:**
_List the values that $$ X $$ may take on. (Separate the values with commas.)_

**Answer:**
$$ x = 140, -30 $$

**Explanation:**
Let's calculate the possible outcomes for the net profit $$ X $$:

1. **If you win the raffle:**
   - **Prize:** \$170
   - **Cost of Tickets:** 5 tickets × \$6 = \$30
   - **Net Profit ($$ X $$):** \$170 - \$30 = \$140

2. **If you don't win the raffle:**
   - **Prize:** \$0
   - **Cost of Tickets:** \$30
   - **Net Profit ($$ X $$):** \$0 - \$30 = -\$30

Therefore, the random variable $$ X $$ can take on two possible values:
$$
x = 140,\ -30
$$

---

### **Summary of Answers**

- **a.** B
- **b.** A
- **c.** 140, -30

If you need further clarification on any part, feel free to ask!
**Part a:** B. The expected value of profit **Part b:** A. The net profit earned by purchasing five tickets. **Part c:** 140, -30

Solución de tutoría real

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Probability Questions