Question

At Central High School, the following probabilities have been determined.

• The probability that a student is enrolled in a foreign language class is equal to f.

• The probability that a student is enrolled in a technology class is equal to g.

• The probability that a student is enrolled in both a foreign language class and a technology class is equal to h.


Which expression can be used to determine the probability that a student is enrolled in a foreign language class, given that the student is enrolled in a technology class?

Answer 1

The expression is
`(h)/(g)`

Explanation:

Define the following events:

A: The student is enrolled in a foreign language class,

B: The student is enrolled in a technology class

We are given that
`P(A) = f, P(B) = g, P(A\cap B) = h`

Recall the definition of conditional probability: Let A, B be sets if P(B)>0, then, the probability of A given B is given by the expression

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

So, using this, we are asked for the probability
`P(A|B)` which is

`P(A|B) = (P(A\cap B))/(P(B)) = (h)/(g)`