Question

If the probability for $A$ to fail in an examination is $0.2$ and that for $B$ 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)$=0.3$
$P(A\cap B)=P\left(A\right)P\left(B\right)=\left(0.2\right)\left(0.3\right)\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=0.2+0.3-0.06=0.44$
Hence, it is a false statement