In a group of 100 students, 40 like Computer Science (group A), 30 like Philosophy (group B), and 20 like both (group A∩B). If a student chosen randomly likes Computer
Science, what is the probability that they also like Philosophy?

Given:

Total number of student = 40

Students who like Computer Science (group A) = 40

Students who like Philosophy (group B) = 30

Students who like both (group A∩B) = 20

To find:

If a student chosen randomly likes Computer  Science, what is the probability that they also like Philosophy?

Solution:

Let the following events,

A: Student like Computer Science

B: Student like Philosophy

Now,

We need to find the probability that the student like Philosophy if it is given that he likes Computer science, i.e, .

Using conditional probability, we get

Therefore, the required probability is 0.5.

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