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,
[tex]P(A)=\dfrac{40}{100}=0.4[/tex]
[tex]P(B)=\dfrac{30}{100}=0.3[/tex]
[tex]P(A\cap B)=\dfrac{20}{100}=0.2[/tex]
We need to find the probability that the student like Philosophy if it is given that he likes Computer science, i.e, [tex]P(\dfrac{B}{A})[/tex].
Using conditional probability, we get
[tex]P(\dfrac{B}{A})=\dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\dfrac{B}{A})=\dfrac{0.2}{0.4}[/tex]
[tex]P(\dfrac{B}{A})=\dfrac{1}{2}[/tex]
[tex]P(\dfrac{B}{A})=0.5[/tex]
Therefore, the required probability is 0.5.
