Question

In a class, 40% of the students like Mathematics and 25% of students like Physics and 15% like both the subjects. One student select at random, find the probability that he likes Physics if it is known that he likes Mathematics.

Answer 1

The probability that a student likes Physics, given that they like Mathematics, is 37.5%.

Step-by-step explanation:

To find the probability that a student likes Physics given that they like Mathematics, we need to use conditional probability. Let's denote the event that a student likes Mathematics as M and the event that a student likes Physics as P. We are given that P(M) = 40% and P(P) = 25%. We also know that P(M and P) = 15%, which represents the percentage of students who like both subjects.

The probability that a student likes Physics given that they like Mathematics can be calculated as:

P(P|M) = P(M and P) / P(M)

Substituting the given values:

P(P|M) = 0.15 / 0.40 = 0.375

Therefore, the probability that the randomly selected student likes Physics, given that they like Mathematics, is 0.375 or 37.5%.