Question

If the probability for $A$ to fail in an examination is $0.2$ and that of $B$ is $0.3$, then the probability that either $A$ or $B$ fails is $0.5$.

Answer 1

Given, $P(A$ fails in examination) $=0.2$
and $P(B$ fails in examination) $=0.3$
$P(A\cap B)=P(A)P(B)=(0.2)(0.3)$
$\therefore P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$=0.2+0.3-0.06=0.44$
Hence, it is a false statement.