Probability — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.91,Page.285

Question

In a college, 30\% students fail in Physics, 25\% fail in Mathematics and 10\% fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in Mathematics is

(a) $\frac{1}{{10}}$
(b) $\frac{2}{5}$ ✓ Correct
(c) $\frac{9}{{20}}$
(d) $\frac{1}{3}$

Step-by-step Solution

Here, ${P_{(Ph)}} = \frac{{30}}{{100}} = \frac{3}{{10}},{P_{(M)}} = \frac{{25}}{{100}} = \frac{1}{4}$

and ${P_{(M \cap Ph)}} = \frac{{10}}{{100}} = \frac{1}{{10}}$

$\therefore$ $P\left( {\frac{{Ph}}{M}} \right) = \frac{{P(Ph \cap M)}}{{P(M)}} = \frac{{1/10}}{{1/4}} = \frac{2}{5}$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.