Answered

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 :

Answer:

The expression is [tex]\frac{h}{g}[/tex]

Step-by-step 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 [tex]P(A) = f, P(B) = g, P(A\cap B) = h[/tex]

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

[tex]P(A|B) = \frac{P(A\cap B)}{P(B)}[/tex]

So, using this, we are asked for the probability [tex]P(A|B)[/tex] which is

[tex]P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{h}{g}[/tex]

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