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14.Probability
medium
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
