Question

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ are two non-empty events of the experiment. If $A$ consists of $4$ outcomes, then number of possible outcomes that $B$ must have so that $A$ and $B$ are independent is/are ?

• A. $2$
• B. $4$
• C. $5$
• D. $10$

Answer 1

Answer: (C), (D)

$10$

Let $n_B$ and $n_{A\cap B}$ denote the number of outcomes favourable to $B$ and $A\cap B$ respectively.
As $A$ and $B$ are independent.
$\Rightarrow P(A\cap B)=P\left(A\right)\cdot P\left(B\right)\Rightarrow \frac{n_{A\cap B}}{10}=\frac{4}{10}\times \frac{n_B}{10}\Rightarrow 5n_{A\cap B}=2n_B\Rightarrow n_B=5\text{or}10[\because 1\le n_B\le 10]$