If one order is selected, find the probability of getting an order from Restaurant A or an order that is accurate Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events? The probability of getting an order from Restaurant A or an order that is accurate is (Round to three decimal places as needed.) CEES

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### Drive-thru Order Accuracy Analysis

**Objective:** Examine the probability of receiving an accurate order from a drive-thru restaurant, or specifically from Restaurant A.

#### Data Table

The table below summarizes the accuracy of drive-thru orders at four different popular fast food chains, labeled A through D.

|                          | Drive-thru Restaurant                     |
|--------------------------| A        | B         | C         | D         |
|---------------------------| ------- | -------- | --------| ------- |
| **Order Accurate**       | 337   | 268    | 250    | 146    |
| **Order Not Accurate** | 46     | 50      | 39      | 10       |

#### Analysis Task

**Question:** If one order is selected, what is the probability of getting an order from Restaurant A, **or** an order that is accurate? Additionally, are the events of selecting an order from Restaurant A and selecting an accurate order disjoint?

To find the probability, we employ the principle of probability for non-disjoint events.

#### Probabilities

1. Total number of orders = Sum of all entries in the table
    - \(337 + 268 + 250 + 146 + 46 + 50 + 39 + 10 = 1146\)
2. Probability of selecting an order from Restaurant A (P(A)):
    - \((337 + 46)/1146 = 383/1146\)
    - \(P(A) ≈ 0.334\) (rounded to three decimal places)
3. Probability of selecting an accurate order (P(Accurate)):
    - \((337 + 268 + 250 + 146)/1146 = 1001/1146\) 
    - \(P(Accurate) ≈ 0.873\) (rounded to three decimal places)
4. Probability of selecting an accurate order from Restaurant A (P(A and Accurate)):
    - \(337/1146\)
    - \(P(A and Accurate) ≈ 0.294\) (rounded to three decimal places)

5. **Combined Probability \(P(A \cup Accurate)\):**
    - \(P(A) + P(Accurate) - P(A and Accurate)\)
    - \(P(A \cup Accurate) ≈ 0.334 + 0.873 - 0.294\)
    - \(P(A \cup Accurate)
Transcribed Image Text:### Drive-thru Order Accuracy Analysis **Objective:** Examine the probability of receiving an accurate order from a drive-thru restaurant, or specifically from Restaurant A. #### Data Table The table below summarizes the accuracy of drive-thru orders at four different popular fast food chains, labeled A through D. | | Drive-thru Restaurant | |--------------------------| A | B | C | D | |---------------------------| ------- | -------- | --------| ------- | | **Order Accurate** | 337 | 268 | 250 | 146 | | **Order Not Accurate** | 46 | 50 | 39 | 10 | #### Analysis Task **Question:** If one order is selected, what is the probability of getting an order from Restaurant A, **or** an order that is accurate? Additionally, are the events of selecting an order from Restaurant A and selecting an accurate order disjoint? To find the probability, we employ the principle of probability for non-disjoint events. #### Probabilities 1. Total number of orders = Sum of all entries in the table - \(337 + 268 + 250 + 146 + 46 + 50 + 39 + 10 = 1146\) 2. Probability of selecting an order from Restaurant A (P(A)): - \((337 + 46)/1146 = 383/1146\) - \(P(A) ≈ 0.334\) (rounded to three decimal places) 3. Probability of selecting an accurate order (P(Accurate)): - \((337 + 268 + 250 + 146)/1146 = 1001/1146\) - \(P(Accurate) ≈ 0.873\) (rounded to three decimal places) 4. Probability of selecting an accurate order from Restaurant A (P(A and Accurate)): - \(337/1146\) - \(P(A and Accurate) ≈ 0.294\) (rounded to three decimal places) 5. **Combined Probability \(P(A \cup Accurate)\):** - \(P(A) + P(Accurate) - P(A and Accurate)\) - \(P(A \cup Accurate) ≈ 0.334 + 0.873 - 0.294\) - \(P(A \cup Accurate)
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