Question

1. alberto surveyed the students in his homeroom and asked if they were studying spanish, french, both, or neither. the probability that a student is studying both spanish and french is 0.16, the probability that a student is studying spanish is 0.64, and the probability that a student is studying french is 0.4. what is the probability that a student is studying french, given that the student is studying spanish?

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 is studying French and $B$ be the event that a student is studying Spanish.

Step2: Identify given probabilities

We are given that $P(A\cap B) = 0.16$ (probability of studying both French and Spanish) and $P(B)=0.64$ (probability of studying Spanish).

Step3: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.16}{0.64}=\frac{1}{4}=0.25$.

Answer:

$0.25$