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Home  >>  CBSE XI  >>  Math  >>  Probability

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 for neither NCC or NSS

$\begin{array}{1 1}(A)\;\large\frac{11}{30}\\(B)\;\large\frac{19}{30}\\(C)\;\large\frac{19}{30}\\(D)\;\text{None of these}\end{array} $

1 Answer

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:
P(Students has opted neither NCC or NSS)
$\Rightarrow 1-P$(Students opted for NCC or NSS)
$\Rightarrow 1-\large\frac{38}{60}$
$\Rightarrow \large\frac{60-38}{60}$
$\Rightarrow \large\frac{22}{60}$
$\Rightarrow \large\frac{11}{30}$
Hence (A) is the correct answer.
answered Jul 2, 2014 by sreemathi.v
 

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