In a class of 60 students,30 opted for NCC,32 | vedclass

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Question

(A) Let $A$ be the event that the selected student opted for $NCC$ and $B$ be the event that the selected student opted for $NSS$.Total number of stud

Vedclass · Accepted Answer

$\frac{11}{30}$

Vedclass · Answer

(A) Let $A$ be the event that the selected student opted for $NCC$ and $B$ be the event that the selected student opted for $NSS$.Total number of students $n(S) = 60$.Number of students who opted for $NCC$,$n(A) = 30$.Number of students who opted for $NSS$,$n(B) = 32$.Number of students who opted for both,$n(A \cap B) = 24$.The number of students who opted for $NCC$ or $NSS$ is given by $n(A \cup B) = n(A) + n(B) - n(A \cap B) = 30 + 32 - 24 = 38$.The number of students who opted for neither $NCC$ nor $NSS$ is $n(A' \cap B') = n(S) - n(A \cup B) = 60 - 38 = 22$.The probability that the student opted for neither is $P(A' \cap B') = \frac{n(A' \cap B')}{n(S)} = \frac{22}{60} = \frac{11}{30}$.

In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student has opted for neither $NCC$ nor $NSS$.

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