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 ma…

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asked Sep 6, 2022 78.0k views

1 Answer

Vladimir Liubimov · Answer 1 · 2022-09-13T03:06:56+0000

Answer:

500 students appeared in the examination.

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 = (300)/(0.6)

t = 500

500 students appeared in the examination.