To find the probability that a randomly chosen customer purchased a truck or a white car, let's work through the problem step-by-step.
### Step 1: Calculate Total Number of Customers
First, we need to determine the total number of customers by summing up all the purchases recorded:
- Red Sedan: 17
- Red SUV: 7
- Red Truck: 3
- Blue Sedan: 17
- Blue SUV: 19
- Blue Truck: 23
- White Sedan: 43
- White SUV: 37
- White Truck: 53
Total customers = [tex]\( 17 + 7 + 3 + 17 + 19 + 23 + 43 + 37 + 53 = 219 \)[/tex]
### Step 2: Calculate the Number of Customers Who Purchased a Truck
Next, let's sum up the number of customers who purchased a truck:
- Red Truck: 3
- Blue Truck: 23
- White Truck: 53
Total truck customers = [tex]\( 3 + 23 + 53 = 79 \)[/tex]
### Step 3: Calculate the Number of Customers Who Purchased a White Car
Now, we need to sum the number of customers who purchased a white car (including sedans, SUVs, and trucks):
- White Sedan: 43
- White SUV: 37
- White Truck: 53
Total white car customers = [tex]\( 43 + 37 + 53 = 133 \)[/tex]
### Step 4: Determine the Number of Customers Who Purchased Either a Truck or a White Car
We must ensure we don't double-count customers who purchased white trucks, as they have been included in both the "truck" and "white car" categories. We already counted white trucks in both categories:
White trucks: 53
So we add the number of truck customers and white car customers, then subtract the white trucks to ensure they're not counted twice:
Total who purchased a truck or it is white = [tex]\( (79 + 133 - 53) = 159 \)[/tex]
### Step 5: Calculate the Probability
Finally, the probability that a randomly chosen customer purchased either a truck or a white car is the number of such customers divided by the total number of customers:
[tex]\[ P(\text{White or Truck}) = \frac{\text{Number of customers who purchased either a truck or a white car}}{\text{Total number of customers}} \][/tex]
[tex]\[ P(\text{White or Truck}) = \frac{159}{219} \][/tex]
### Conclusion
Therefore, the probability that a randomly chosen customer purchased a truck or a white car is approximately [tex]\( 0.726 \)[/tex] or in simplest form, [tex]\( \frac{159}{219} \)[/tex].
