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# If the probabilities 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

$\begin{array}{1 1}(A)\; > .5\\(B)\;.5\\(C)\;\leq .5\\(D)\;0\end{array}$

Can you answer this question?

Toolbox:
• $P(A\cup B)=P(A)+P(B)-P(A \cap B)$
We know that $P(A\cup B)=P(A)+P(B)-P(A \cap B)$
$\therefore$ P(Either A or B fails )=0.2+0.3=0.5
$P(A\cap B)$ is not available and $P(A\cap B)$ is always subtracted
$\therefore \leq 0.5$
Hence (C) is the correct answer.
answered Jul 9, 2014