To find the probability that a randomly selected vehicle is white given that it is an SUV, [tex]\( P(\text{White} \mid \text{SUV}) \)[/tex], we need to use the formula for conditional probability. This is expressed as:
[tex]\[
P(\text{White} \mid \text{SUV}) = \frac{P(\text{White and SUV})}{P(\text{SUV})}
\][/tex]
From the two-way table provided, we can extract the following information:
- The total number of SUVs observed ([tex]\( P(\text{SUV}) \)[/tex]) is 35.
- The number of white SUVs ([tex]\( P(\text{White and SUV}) \)[/tex]) is 22.
Now, we compute the conditional probability:
[tex]\[
P(\text{White} \mid \text{SUV}) = \frac{22 \text{ white SUVs}}{35 \text{ total SUVs}}
\][/tex]
To convert this fraction into a percentage, we perform the division and then multiply by 100:
[tex]\[
P(\text{White} \mid \text{SUV}) = \left(\frac{22}{35}\right) \times 100
\][/tex]
Performing the division:
[tex]\[
\frac{22}{35} \approx 0.6285714285714286
\][/tex]
Multiplying by 100 to convert to a percentage:
[tex]\[
0.6285714285714286 \times 100 \approx 62.857142857142854
\][/tex]
Rounding to the nearest whole percent:
[tex]\[
P(\text{White} \mid \text{SUV}) \approx 63\%
\][/tex]
Therefore, the probability that a randomly selected vehicle is white given that it is an SUV is approximately:
[tex]\[
\boxed{63\%}
\][/tex]
