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.