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14.Probability
hard
In a class of $60$ students, $40$ opted for $NCC,\,30$ opted for $NSS$ and $20$ opted for both $NCC$ and $NSS.$ If one of these students is selected at random, then the probability that the student selected has opted neither for $NCC$ nor for $NSS$ is
A
$\frac {1}{6}$
B
$\frac {1}{3}$
C
$\frac {2}{3}$
D
$\frac {5}{6}$
(JEE MAIN-2019)
Solution
$A \rightarrow$ opted $\mathrm{NCC}$
$\mathrm{B} \rightarrow$ opted $\mathrm{NSS}$
$\therefore $ $P \text { (neither } A \text { nor } B)=\frac{10}{60}=z \frac{1}{6}$
Standard 11
Mathematics
