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A student observed the color and type of vehicle that passed by his school for an hour. The two-way table is given below:

| | Red | Blue | White | Total |
|------|-----|------|-------|-------|
| Car | 19 | 6 | 7 | 32 |
| Truck| 8 | 16 | 9 | 33 |
| SUV | 3 | 10 | 22 | 35 |
| Total| 30 | 32 | 38 | 100 |

What is the probability that a randomly selected vehicle from this observation is white, given that it's an SUV?

[tex]\( P(\text{White} \mid \text{SUV}) = [?] \% \)[/tex]

Round your answer to the nearest whole percent.



Answer :

GinnyAnswer
To find the conditional probability [tex]\( P(\text{White} \mid \text{SUV}) \)[/tex], we need to determine the probability that a vehicle is white, given that it is an SUV.

Here's the step-by-step process:

1. Determine the total number of SUVs observed: According to the table, the total number of SUVs observed is 35.

2. Determine the number of white SUVs observed: From the table, we see that the number of white SUVs observed is 22.

3. Calculate the conditional probability [tex]\( P(\text{White} \mid \text{SUV}) \)[/tex]:
[tex]\[ P(\text{White} \mid \text{SUV}) = \frac{\text{Number of white SUVs}}{\text{Total number of SUVs}} \][/tex]
Plugging in our numbers:
[tex]\[ P(\text{White} \mid \text{SUV}) = \frac{22}{35} \][/tex]

4. Convert the fraction to a percentage:
[tex]\[ \frac{22}{35} \approx 0.6285714285714286 \][/tex]
To convert this to a percentage, we multiply by 100:
[tex]\[ 0.6285714285714286 \times 100 \approx 62.857142857142854\% \][/tex]

5. Round to the nearest whole percent:
[tex]\[ 62.857142857142854\% \approx 63\% \][/tex]

Therefore, the probability that a randomly selected vehicle is white, given that it is an SUV, rounded to the nearest whole percent, is 63%.

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