Question

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

• A. 2, 4 or 8
• B. 3, 6 or 9
• C. 4 or 8
• D. 5 or 10

Answer 1

Answer: (D)

$P(A\cap B)=\frac{4}{10}\times \frac{p}{10}=\frac{2p/5}{10}$
$\Rightarrow \frac{2p}{5}$ is an integer
$\Rightarrow p=5$ or 10