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.
​Drive-thru Restaurant
A
B
C
D
Order Accurate
324
273
232
148
Order Not Accurate
37
50
32
18
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?
Question content area bottom
Part 1
The probability of getting an order from Restaurant A or an order that is accurate is

enter your response here.
​(Round to three decimal places as​ needed.)
Part 2
Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint​ events?
The events
▼
are not
are
disjoint because it
▼
is not
is
possible to
▼
pick an inaccurate order.
pick an order from Restaurant B, C, or D.
receive an accurate order from Restaurant A.

### Part 1: Probability of getting an order from Restaurant A or an order that is accurate

To solve this, we need to use the formula for the probability of the union of two events \( A \) and \( B \), which is:

\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
\]

Where:
- \( P(A) \) is the probability of selecting an order from Restaurant A.
- \( P(B) \) is the probability of selecting an accurate order.
- \( P(A \text{ and } B) \) is the probability of selecting an accurate order from Restaurant A (i.e., the intersection of the two events).

First, let's calculate the total number of orders:

\[
\text{Total Orders} = (324 + 273 + 232 + 148) + (37 + 50 + 32 + 18) = 977
\]

#### Step 1: Probability of selecting an order from Restaurant A, \( P(A) \):

The number of orders from Restaurant A is:

\[
P(A) = \frac{\text{Orders from A}}{\text{Total Orders}} = \frac{324 + 37}{977} = \frac{361}{977} \approx 0.369
\]

#### Step 2: Probability of selecting an accurate order, \( P(B) \):

The number of accurate orders is:

\[
P(B) = \frac{\text{Total Accurate Orders}}{\text{Total Orders}} = \frac{324 + 273 + 232 + 148}{977} = \frac{977}{977} = 0.977
\]

#### Step 3: Probability of selecting an accurate order from Restaurant A, \( P(A \text{ and } B) \):

The number of accurate orders from Restaurant A is 324. So:

\[
P(A \text{ and } B) = \frac{324}{977} \approx 0.332
\]

#### Step 4: Calculate the probability of getting an order from Restaurant A or an accurate order:

\[
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = 0.369 + 0.977 - 0.332 = 1.014
\]

Since probabilities cannot exceed 1, this result indicates that the total probability is essentially 1, meaning that getting an order from Restaurant A or an accurate order is highly likely.

### Part 2: Are the events disjoint?

Two events are disjoint if they cannot happen at the same time. In this case, it **is possible** to select an order from Restaurant A and for that order to be accurate (i.e., you can have both events occur simultaneously).

Thus, the events **are not disjoint** because it is possible to receive an accurate order from Restaurant A.

---

### Summary:

- The probability of getting an order from Restaurant A or an order that is accurate is approximately **1** (rounded to three decimal places).
- The events **are not disjoint** because it is possible to receive an accurate order from Restaurant A.

---

Would you like further details or have any other questions? Here are some related questions for further exploration:

1. What is the probability of getting an order from Restaurant B or an accurate order?
2. How would the probability change if the total number of orders increased?
3. What is the probability of getting an inaccurate order from Restaurant C?
4. What is the combined probability of selecting an accurate order from Restaurants A and D?
5. If you randomly select two orders, what is the probability that both are accurate?

**Tip:** When dealing with "or" probabilities, remember to subtract the overlap (intersection) to avoid double-counting!

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. 
Drive-thru Restaurant: A, B, C, D 
Order Accurate: 324, 273, 232, 148 
Order Not Accurate: 37, 50, 32, 18
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?

Learn how to calculate the probability of selecting an order from Restaurant A or getting an accurate order based on fast food drive-thru data. Explore probability concepts and the formula for union of events. Suitable for students in Grades 10-12.

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