Chances to fail in Physics are 20% and chances to fail in Mathematics are 10% . What are chances to

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14.Probability

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The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject ............ $\%$

A

$28$

B

$38$

C

$72$

D

$82$

Solution

(a) Let $P(A) = \frac{{20}}{{100}} = \frac{1}{5},$ $P(B) = \frac{{10}}{{100}} = \frac{1}{{10}}$

Since events are independent and we have to find

$P(A \cup B) = P(A) + P(B) – P(A)\,.\,P(B)$

$ = \frac{1}{5} + \frac{1}{{10}} – \frac{1}{5} \times \frac{1}{{10}} = \frac{3}{{10}} – \frac{1}{{50}} $

$= \frac{{14}}{{50}} = \frac{{14}}{{50}} \times 100 = 28\% .$

Standard 11

Mathematics

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