Let's break down the problem step by step.
### Step 1: Calculate the total number of orders for each restaurant
From the given data:
- Restaurant A: 322 accurate + 35 not accurate = 357 total orders
- Restaurant B: 280 accurate + 52 not accurate = 332 total orders
- Restaurant C: 243 accurate + 38 not accurate = 281 total orders
- Restaurant D: 140 accurate + 17 not accurate = 157 total orders
### Step 2: Calculate the total number of orders
Adding up the total orders from all restaurants:
[tex]\[
357 + 332 + 281 + 157 = 1127
\][/tex]
There are 1127 total orders.
### Step 3: Calculate the probabilities
#### 3.1 Probability of getting an order from Restaurant A
[tex]\[
\text{Probability of A} = \frac{\text{Total orders from A}}{\text{Total orders}} = \frac{357}{1127} \approx 0.317
\][/tex]
#### 3.2 Probability of getting an accurate order
Adding up the accurate orders from all restaurants:
[tex]\[
322 + 280 + 243 + 140 = 985
\][/tex]
[tex]\[
\text{Probability of accurate order} = \frac{\text{Total accurate orders}}{\text{Total orders}} = \frac{985}{1127} \approx 0.874
\][/tex]
#### 3.3 Probability of getting an accurate order from Restaurant A
[tex]\[
\text{Probability of accurate order from A} = \frac{\text{Accurate orders from A}}{\text{Total orders}} = \frac{322}{1127} \approx 0.286
\][/tex]
### Step 4: Calculate the probability of getting an order from Restaurant A or an order that is accurate
Using the formula [tex]\( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \)[/tex]:
[tex]\[
P(A \text{ or Accurate}) = P(A) + P(\text{Accurate}) - P(A \text{ and Accurate})
\][/tex]
[tex]\[
P(A \text{ or Accurate}) = 0.317 + 0.874 - 0.286 = 0.905
\][/tex]
So, the probability of getting an order from Restaurant A or an order that is accurate is:
[tex]\[
\boxed{0.905}
\][/tex]
### Step 5: Check if the events are disjoint
Two events are disjoint if they cannot occur simultaneously. Here, selecting an order from Restaurant A and selecting an accurate order can indeed occur at the same time, as seen from the probability calculation for accurate orders from A.
Therefore, the events of selecting an order from Restaurant A and selecting an accurate order are not disjoint.
### Summary:
- The probability of getting an order from Restaurant A or an order that is accurate is [tex]\( \boxed{0.905} \)[/tex].
- The events of selecting an order from Restaurant A and selecting an accurate order are not disjoint.
