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Read the following passage and answer the questions given below
In pre-board examination of class XII, commerce stream with Economics and Mathematics of a particular school, 50% of the students failed in Economics, 35% failed in Mathematics and 25% failed in both Economics and Mathematics. A student in selected at random from the class.
Question:
Find the probability that the selected student has failed in Economics but pass in mathematics

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$\frac{2}{19}$

$\frac{13}{40}$

$\frac{3}{40}$

$\frac{5}{6}$

answer is B.

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Detailed Solution

Let E = student has failed in Economics, M =student has failed in Mathematics $∴ P (E) = \frac{50}{100} = \frac{1}{2}, P (M) = \frac{35}{100} = \frac{7}{20}$

Now

$P (E \cap M) = P (E) . P (M) = \frac{1}{2} \times \frac{13}{20} = \frac{13}{40}$

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