NIMCET 2016 — Mathematics PYQ

Concept: 

Let $S$ be the sample space. $A$ be any event then  

$P(A)=\frac{n(A)}{n(S)}$  

The experiment $A$ and $B$ are independent.  

$\Rightarrow P(A\cap B)=P(A)\cdot P(B)$  

Calculations:

Given, an experiment has 10 equally likely outcomes.  
Let $A$ and $B$ be two non-empty events of the experiment.  
$n(B)$ and $n(A\cap B)$ be the number of outcomes of experiment $B$ and $A\cap B$ respectively.  

As the experiment $A$ and $B$ are independent,  

$\Rightarrow P(A\cap B)=P(A)\cdot P(B)$  

$\Rightarrow \frac{n(A\cap B)}{10}=\frac{n(A)}{10}\cdot \frac{n(B)}{10}$  

$\Rightarrow n(A\cap B)=\frac{n(A)\cdot n(B)}{10}$  

Given $n(A)=4$, so  

$\Rightarrow n(A\cap B)=\frac{4}{10}\cdot n(B)$  

$\Rightarrow n(A\cap B)=\frac{2}{5}\cdot n(B)$  

$\Rightarrow 5n(A\cap B)=2n(B)$  

$\Rightarrow n(B)=5\text{ or }10$  

Hence, an experiment has 10 equally likely outcomes.  
Let $A$ and $B$ be two non-empty events of the experiment.  
If $A$ consists of 4 outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent is **5 or 10**.