To find \( P(V \mid S) \), we need to determine the conditional probability that a vehicle is an SUV (V) given that it is from Somerset (S). This can be calculated using the formula for conditional probability:
[tex]\[ P(V \mid S) = \frac{P(V \cap S)}{P(S)} \][/tex]
Where:
- \( P(V \cap S) \) is the probability that a vehicle is both an SUV and from Somerset.
- \( P(S) \) is the probability that a vehicle is from Somerset.
First, let's identify the values from the contingency table.
1. The number of SUVs (V) in Somerset (S) is 19.
2. The total number of vehicles in Somerset (S) is 100.
Now, we calculate \( P(V \mid S) \) using these values.
[tex]\[ P(V \mid S) = \frac{\text{Number of SUVs in Somerset}}{\text{Total number of vehicles in Somerset}} \][/tex]
[tex]\[ P(V \mid S) = \frac{19}{100} \][/tex]
Thus, the conditional probability that a vehicle is an SUV given that it is from Somerset is:
[tex]\[ P(V \mid S) = 0.19 \][/tex]
