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In a class $40 %$ students study mathematics $25 %$ study chemistry and $15 %$ both mathematics and chemistry. If a student is chosen at random the probability that he studies mathematics, If it is known that he studies chemistry is

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a

$\frac{3}{5}$

b

$\frac{1}{8}$

c

$\frac{3}{8}$

d

$\frac{2}{5}$

answer is D.

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Detailed Solution

$\begin{array}{l} P (M) = \frac{40}{100} = \frac{2}{5} \\ P (C) = \frac{25}{100} = \frac{1}{4} \\ P (M \cap C) = \frac{15}{100} = \frac{6}{20} \\ ∴ P (\frac{M}{C}) = \frac{P (M \cap C)}{P (C)} = \frac{\frac{3}{20}}{\frac{1}{4}} = \frac{3}{5} \end{array}$

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