Chapter 4 HW - Discrete Random Variable +A! Category: Homework b. Find the probability that a customer rents three DVDs. (Give your answer as a decimal) Answer: Enter your answer c. Find the probability that a customer rents at least one DVD. (Give your answer as a decimal) Answer: Enter your answer d. Find the probability that a customer rents at most two DVDs. (Give your answer as a decimal) Answer: Enter your answer Submit answer Attempts: 0/10 Find this question difficult? Do you know you can practice another version of this question?

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UpStudy AI · Accepted Answer

To solve the problems regarding the discrete random variable of DVD rentals, we need to know the probability distribution of the number of DVDs rented by a customer. However, since the specific probabilities or distribution are not provided in your question, I will outline the general approach to find the probabilities for parts b, c, and d.

### Known Conditions
1. We need to find:
   - Probability of renting exactly 3 DVDs (part b).
   - Probability of renting at least 1 DVD (part c).
   - Probability of renting at most 2 DVDs (part d).

### General Approach
1. **Define the Random Variable**: Let $$ X $$ be the random variable representing the number of DVDs rented by a customer.
2. **Probability Distribution**: We need the probability mass function (PMF) $$ P(X = k) $$ for $$ k = 0, 1, 2, 3, \ldots $$ (the number of DVDs rented).
3. **Calculate Probabilities**:
   - For part b, find $$ P(X = 3) $$.
   - For part c, find $$ P(X \geq 1) = 1 - P(X = 0) $$.
   - For part d, find $$ P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) $$.

### Steps to Solve
1. **Find $$ P(X = 3) $$**: This is directly from the PMF.
2. **Find $$ P(X = 0) $$**: This is also from the PMF.
3. **Calculate $$ P(X \geq 1) $$**: Use the result from $$ P(X = 0) $$.
4. **Calculate $$ P(X \leq 2) $$**: Sum the probabilities for $$ P(X = 0) $$, $$ P(X = 1) $$, and $$ P(X = 2) $$.

### Example Calculation
Assuming we have the following PMF:
- $$ P(X = 0) = p_0 $$
- $$ P(X = 1) = p_1 $$
- $$ P(X = 2) = p_2 $$
- $$ P(X = 3) = p_3 $$

Then:
- For part b: $$ P(X = 3) = p_3 $$
- For part c: $$ P(X \geq 1) = 1 - p_0 $$
- For part d: $$ P(X \leq 2) = p_0 + p_1 + p_2 $$

### Conclusion
To provide specific decimal answers, please provide the probability distribution or the values of $$ P(X = k) $$ for $$ k = 0, 1, 2, 3 $$. Once I have that information, I can calculate the exact probabilities for parts b, c, and d.
Cannot determine the probabilities without the probability distribution of the number of DVDs rented by a customer.

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