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

Answer:

5000 students appeared in the examination.

Step-by-step 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

$0.6t = 3000$

$t = \frac{3000}{0.6}$

$t = 5000$

5000 students appeared in the examination.