Question

out of some students appeared in an examination 80% passed in mathematics 75% passed in english and 5% failed in both subjects if 3000 of them were passed both subjects how many students were appeared i the examination find by using a venn diagram​

Answer 1

5000 students appeared in the examination.

Explanation:

We solve this question using Venn probabilities.

I am going to say that:

Event A: Passed in Mathematics

Event B: Passed in English.

5% failed in both subjects

This means that 100 - 5 = 95% pass in at least one, which means that
`P(A \cup B) = 0.95`

80% passed in mathematics 75% passed in english

This means that
`P(A) = 0.8, P(B) = 0.75`

Proportion who passed in both:

`P(A \cap B) = P(A) + P(B) - P(A \cup B)`

Considering the values we have for this problem

`P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.8 + 0.75 - 0.95 = 0.6`

3000 of them were passed both subjects how many students appeared in the examination?

3000 is 60% of the total t. So

`0.6t = 3000`

`t = (3000)/(0.6)`

`t = 5000`

5000 students appeared in the examination.