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

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Question

(A) Let $A$ be the event that the selected student has opted for $NCC$ and $B$ be the event that the selected student has opted for $NSS$.
Total numbe

Vedclass · Accepted Answer

$\frac{2}{15}$

Vedclass · Answer

(A) Let $A$ be the event that the selected student has opted for $NCC$ and $B$ be the event that the selected student has opted for $NSS$.
Total number of students $= 60$.
Number of students who have opted for $NCC$, $n(A) = 30$.
Number of students who have opted for $NSS$, $n(B) = 32$.
Number of students who have opted for both $NCC$ and $NSS$, $n(A \cap B) = 24$.
We need to find the probability that the student has opted for $NSS$ but not $NCC$, which is $P(B - A)$.
The number of students who have opted for $NSS$ but not $NCC$ is given by $n(B - A) = n(B) - n(A \cap B)$.
$n(B - A) = 32 - 24 = 8$.
The probability is $P(B - A) = \frac{n(B - A)}{	ext{Total students}} = \frac{8}{60}$.
Simplifying the fraction, we get $\frac{8}{60} = \frac{2}{15}$.

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 $NSS$ but not $NCC$.

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