# 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

$\begin {array} {1 1} (A)\;0.38 & \quad (B)\;0.44 \\ (C)\;0.50 & \quad (D)\;0.94 \end {array}$

$P( \overline A) = 0.2$
$P(A) = 1-0.2$
= $0.8$
$P( \overline B) = 0.3$
$P(B) = 1-0.3 = 0.7$
$P( \overline A \cup \overline B) = P( \overline {A \cap B })$
$= 1-P(A \cap B )$
$1-P(A)\: P(B)$
$1-(0.8)(0.7)$
$= 0.44$
Ans : B