Question

In a school, 78% of the students take a foreign language class, and 33% of students take both foreign language and technology class. What is the probability that a student takes a technology class, given that the student takes the foreign language class?

Answer 1

The probability that a student takes a technology class, given that the student takes the foreign language class, is approximately 0.4231 (or 42.31%).

Step-by-step explanation:

To find the probability that a student takes a technology class, given that the student takes the foreign language class, we can use conditional probability.

Let's denote the probability of taking a foreign language class as P(F) and the probability of taking both foreign language and technology class as P(F ∩ T).

The formula for conditional probability is:

P(T|F) = P(F ∩ T) / P(F)

In this case, P(F) is given as 78% (0.78) and P(F ∩ T) is given as 33% (0.33).

Plugging in the values, we can calculate:

P(T|F) = 0.33 / 0.78

= 0.4231

Therefore, the probability that a student takes a technology class, given that the student takes the foreign language class, is approximately 0.4231 (or 42.31%).