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WAEC Mathematics 2017 Paper

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Question : 43

Total: 49

In a class of 45 students, 28 offer chemistry and 25 offer Biology. If each student offers at least one of the two subjects, calculate the probability that a student selected at random from the class the class offers chemistry only.

$\;\frac{2}{9}$
$\;\frac{4}{9}$
$\;\frac{5}{9}$
$\;\frac{7}{9}$

Solution:

Concept:

Use set theory with two overlapping groups to find the number of students taking only Chemistry.

Explanation:

Let

x

be the number of students offering both Chemistry and Biology.

Chemistry only

= 28 - x

Biology only

= 25 - x

Total students

= (28 - x) + x + (25 - x) = 45

This simplifies to

53 - x = 45

So

x = 8

Chemistry only

= 28 - 8 = 20

Probability

= \frac{20}{45} = \frac{4}{9}

Answer:

\frac{4}{9}

(Option B)

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