Question

Out of some students appeared in an examination,
80% passed in English, 75% passed in Science and
5% failed in both subjects. If 300 of them were
passed in both subjects, how many students were
appeared in the examination? Find it by using a
Venn-diagram
(Ans: 500​

Answer 1

Answer:

500 students appeared in the examination.

Step-by-step explanation:

Each event represents a set in the Venn diagram, and we use it to find the desired values.

I am going to say that:

Event A: Passed in English.

Event B: Passed in Science.

80% passed in English

This means that $P(A) = 0.8$.

75% passed in Science

This means that $P(B) = 0.75$

5% failed in both subjects.

This means that 100% - 5% = 95% passed at least one of these subjects, so $P(A \cup B) = 0.95$.

Proportion that passed both subjects:

This is $P(A \cap B)$

These percentages are related by the following equation:

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

So

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

Number of students in class:

60% of the total number t passed both subjects. This is equals to 300. So

$0.6t = 300$

$t = \frac{300}{0.6}$

$t = 500$

500 students appeared in the examination.