Question

in a class, 60% of the students like math, and 40% like science. 20% of the students like both math and science. what is the probability that a student likes science given that they like math?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, event \(A\) is "likes science" and event \(B\) is "likes math".

Step2: Identify the values

We are given that \(P(B) = 0.6\) (probability of liking math) and \(P(A\cap B)=0.2\) (probability of liking both math and science).

Step3: Substitute into the formula

Substitute the values into the formula \(P(A|B)=\frac{0.2}{0.6}=\frac{2}{6}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)