Question

A high school offers both Spanish and French classes. The probability that a student takes both Spanish and French is 0.24. The probability that a student takes Spanish given that the student takes French is 0.32.



What is the probability that a student takes French?

Answer options with 4 options
A.
0.01

B.
0.08

C.
0.56

D.
0.75

Answer 1

To find the probability that a student takes French, we can use the formula for conditional probability.

Let:
- \( P(S \cap F) \) = Probability that a student takes both Spanish and French = 0.24
- \( P(S|F) \) = Probability that a student takes Spanish given that the student takes French = 0.32
- \( P(F) \) = Probability that a student takes French

According to the formula of conditional probability, we have:

\[
P(S|F) = \frac{P(S \cap F)}{P(F)}
\]

We can rearrange this formula to solve for \( P(F) \):

\[
P(F) = \frac{P(S \cap F)}{P(S|F)}
\]

Substituting in the values we have:

\[
P(F) = \frac{0.24}{0.32}
\]

Calculating this:

\[
P(F) = 0.75
\]

So, the probability that a student takes French is \( P(F) = 0.75 \).

Therefore, the correct answer is:

**D. 0.75**