Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Order Accurate Order Not Accurate Drive-thru Restaurant с 233 36 A 335 37 B 260 51 D 126 11 If two orders are selected, find the probability that they are both from Restaurant D. a. Assume that the selections are made with replacement. Are the events independent? b. Assume that the selections are made without replacement. Are the events independent? C a. Assume that the selections are made with replacement. Are the events independent? The probability of getting two orders from Restaurant D is probability of the choice of the second order. (Do not round until the final answer. Round to four decimal places as needed.) The events independent because choosing the first order the

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**Drive-Thru Order Accuracy Study**

The following table details the accuracy of drive-thru orders at various fast food chains. The table represents a random selection of orders and highlights whether they were accurate:

| Drive-thru Restaurant | A   | B   | C   | D   |
|-----------------------|-----|-----|-----|-----|
| Order Accurate        | 335 | 260 | 233 | 126 |
| Order Not Accurate    | 37  | 51  | 36  | 11  |

**Problem Statement:** 

If two orders are selected, calculate the probability that both orders are from Restaurant D.

**Questions:**
a. Assume selections are made with replacement. Are the events independent?  
b. Assume selections are made without replacement. Are the events independent?

---

**Solution Guide:**

a. **With Replacement:**
   - Determine if the events are independent.
   - Calculation: Find the probability of selecting two accurate orders from Restaurant D.
   - Explanation: The events are ⬜ independent because choosing the first order ⬜ the probability of the choice of the second order.
   - Probability: [Enter value] (Round to four decimal places as required.)

b. **Without Replacement:**
   - Discuss the nature of event independence and probability in this context.

Note: Interpretations must be substantiated with appropriate reasoning and calculations. Do not round until the final result.
Transcribed Image Text:**Drive-Thru Order Accuracy Study** The following table details the accuracy of drive-thru orders at various fast food chains. The table represents a random selection of orders and highlights whether they were accurate: | Drive-thru Restaurant | A | B | C | D | |-----------------------|-----|-----|-----|-----| | Order Accurate | 335 | 260 | 233 | 126 | | Order Not Accurate | 37 | 51 | 36 | 11 | **Problem Statement:** If two orders are selected, calculate the probability that both orders are from Restaurant D. **Questions:** a. Assume selections are made with replacement. Are the events independent? b. Assume selections are made without replacement. Are the events independent? --- **Solution Guide:** a. **With Replacement:** - Determine if the events are independent. - Calculation: Find the probability of selecting two accurate orders from Restaurant D. - Explanation: The events are ⬜ independent because choosing the first order ⬜ the probability of the choice of the second order. - Probability: [Enter value] (Round to four decimal places as required.) b. **Without Replacement:** - Discuss the nature of event independence and probability in this context. Note: Interpretations must be substantiated with appropriate reasoning and calculations. Do not round until the final result.
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