Question

The probability that a student takes an English class and a math class is 0.084. The probability that a student takes an English class is 0.49. What is the probability that a student takes a math class given that the student is taking an English class?

Answer 1

we are given the probability of a student taking both classes of 0.084 and the problaity of taking english class of 0.49. The probability  that a student takes a math class given that the student is taking an English class is 0.084/0.49 equal to 0.17

Answer 2

The probability that a student takes a math class given that the student is taking an English class
`P(B/A)=0.17`

Explanation:

Given : The probability that a student takes an English class and a math class is 0.084. The probability that a student takes an English class is 0.49.

To find : What is the probability that a student takes a math class given that the student is taking an English class?

Solution :

Let A be the student takes English class.

Let B be the student take Math class.

Probability that a student takes an English class and a math class is 0.084.

`P(A\cap B)=0.084`

The probability that a student takes an English class is 0.49.

`P(A)=0.49`

We have to find probability that a student takes a math class given that the student is taking an English class
`P(A/B)`

Formula of conditional probability is

`P(B/A)=(P(A\cap B))/(P(A))`

Where B is the probability to find and A is the given condition.

`P(B/A)=(0.084)/(0.49)`

`P(B/A)=0.17`