a high school offers both spanish and french classes. the probability that a student takes both spanish and…
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?\na. 0.01\nb. 0.08\nc. 0.56\nd. 0.75
Answer
Explanation:
Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event that a student takes Spanish and $B$ be the event that a student takes French. We know that $P(A\cap B) = 0.24$ and $P(A|B)=0.32$.
Step2: Rearrange the formula to solve for $P(B)$
From $P(A|B)=\frac{P(A\cap B)}{P(B)}$, we can solve for $P(B)$ by cross - multiplying. We get $P(B)=\frac{P(A\cap B)}{P(A|B)}$.
Step3: Substitute the given values
Substitute $P(A\cap B) = 0.24$ and $P(A|B)=0.32$ into the formula: $P(B)=\frac{0.24}{0.32}=\frac{24}{32}=\frac{3}{4}=0.75$.
Answer:
D. 0.75