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JAMB Mathematics 2024 Paper

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Question : 16

Total: 50

The Venn diagram above shows the number of students offering physics and chemistry in a class of 65. What is the probability that a student selected from the class offers physics and chemistry if every students offers at least one subject?

$\;\frac{2}{13}$
$\;\frac{5}{13}$
$\;\frac{2}{5}$
$\;\frac{3}{13}$

Solution:

Concept:

Use the total number of students in the Venn diagram to find the overlap, then calculate the probability.

Explanation:

Let

x

be the number of students offering both physics and chemistry.

Physics only

= 30 - x

and chemistry only

= 45 - x

.

Since all 65 students offer at least one subject:

(30 - x) + x + (45 - x) = 65

Simplify:

75 - x = 65

x = 10

So, 10 students offer both subjects.

Therefore, the probability is:

\frac{10}{65} = \frac{2}{13}

Answer:

Option A:

\frac{2}{13}

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