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%.
