Question

In a class of 26 students, 15 of them like maths,

13 of them like english and 9 of them don’t like Maths or English
Find the probability that a student chosen at random
likes English but not Maths.

Answer 1

2/13

Explanation:

Easiest way is to draw a Venn diagram

If there are a total of 26 students and 9 of the students don't like Maths or English, then 26 - 9 = 17 students like Maths or English or both

Let m = the number of students who like Maths only

Let e = the number of students who like English only

Let a = the number of students who like BOTH

From the given information:

m + b = 15 ⇒ b = 15 - m

e + b = 13

m + e + b = 17

Substitute b = 15 - m into m + e + b = 17:

⇒ m + e + 15 - m = 17

⇒ e + 15 = 17

⇒ e = 2

Substitute e = 2 into e + b = 13:

⇒ 2 + b = 13

⇒ b = 11

Substitute b = 11 into m + b = 15:

⇒ m + 11 = 15

⇒ m = 4

Now you can draw a Venn diagram (see attached diagram).

Reading from the Venn diagram, the probability that a student likes English but not Maths is 4/26 = 2/13