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# 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 student students is selected at random,find the probability that the student has opted NSS but not NCC

$\begin{array}{1 1}(A)\;\large\frac{2}{15}\\(B)\;\large\frac{3}{15}\\(C)\;\large\frac{4}{15}\\(D)\;\text{None of these}\end{array}$

Toolbox:
• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Step 1:
Given 60 students
n(NCC)=30
n(NSS)=32
$n(NCC\cap NSS)=24$
$\therefore P(NCC)=\large\frac{30}{60}$
$P(NSS)=\large\frac{32}{60}$
$P(NCC \cap NSS)=\large\frac{24}{60}$
Step 2:
The student has opted NSS but not NCC
$\therefore$ P(The student has opted NSS but not NCC)
$\Rightarrow P(NSS)-P(NCC \cap NSS)$
$\Rightarrow \large\frac{32}{60}-\frac{24}{60}$
$\Rightarrow \large\frac{8}{60}$
$\Rightarrow \large\frac{2}{15}$
Hence (A) is the correct answer.