Question

In a high school class, 35% of the students take Spanish as a foreign language, 15% take French as a foreign language, and 40% take at least one of these languages. What is the probability that a randomly chosen student takes French given that the student takes Spanish?

Answer 1

$$P(S)=0.35, P(F)=0.15$$

$$P(S\cup F)=0.40$$

$$P(S\cap F)=P(S)+P(F)-P(S\cup F)$$

$$=0.35+0.15-0.40=0.10$$

$$P(F|S)=\dfrac{P(F\cap S)}{P(S)}=\dfrac{0.10}{0.35}=\dfrac{2}{7}$$