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?

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

Step-by-step 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