Question

The probability that a student takes a history class and a sociology class is 0.051. The probability that a student takes a history class is 0.32. What is the probability that a student takes a sociology class, given that the student is taking a history class?

Answer 1

Answer: 0.159375

Step-by-step explanation:

Let the events are :

H =  Student takes a history class.

S = Student takes a sociology class.

As per given , we have

P(H)=0.32

P(H∩S)=0.051

Now , by using the conditional probability formula , we have

$P(S|H)=\dfrac{P(H\cap S)}{P(H)}\\\\=\dfrac{0.051}{0.32}\\\\=\dfrac{51}{320}=0.159375$

Hence, the probability that a student takes a sociology class, given that the student is taking a history class is 0.159375 .