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  4. 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

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Q. 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

JEE AdvancedJEE Advanced 2008

Solution:

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