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Sagot :
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%.
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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