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
Answer & explanation
Correct answer: option 4
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
$⇒ n = 5, 10.$