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

We have, $P(A)=\frac{4}{10}=\frac{2}{5}$

Suppose B has n outcomes. Then, $P(B)=\frac{n}{10}, 0 < n < 10.$

Since A and B are independent events,

$∴ P(A ∩ B) + P(A) P(B)$

$⇒ P(A ∩ B)=\frac{2}{5}×\frac{n}{10}=\frac{2n/5}{10}$

$⇒ \frac{2n}{5}$ is an integer between 0 and 10

$⇒ \frac{n}{5}$ is an integer between 0 and 5

$⇒ n = 5, 10.$