Question

The probability that a student owns a car is 74%. The probability that a student owns a car or drives to school is 88%. The probability that a student owns a car and drives to school is 56%. Given that the student drives to school, what is the probability that the student owns a car?

Answer 1

The probability that the student owns a car given that the student drives to school is 0.8

Explanation:

Lets put names to each variable

X = The student owns a car

Y = The student drives to school

We alredy know:

P(X) = 0.74

P(X ∪ Y) = 0.88

P(X ∩ Y) = 0.56

And we want to know P(X | Y)

Recall that P(X ∩ Y) = P(X|Y)*P(Y), and also

P(X ∪ Y) = P(X) + P(Y) - P(X∩Y)

Thus,

P(Y) = P(X ∪ Y) - P(X) + P(X ∩ Y) = 0.88-0.74+0.56 = 0.70

And

P(X|Y) = P(X ∩ Y)/P(Y) = 0.56/0.70 = 0.8

Therefore, the probability that the student owns a car given that the student drives to school is 0.8