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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $P(E)$ denote the probability of event $E$.
Given $P(A) = 1$, $P(B) = \frac{1}{2}$, the values of $P(A \mid B)$ and $P(B \mid A)$ respectively are
Solution
Since $P(A)=1$, event $A$ is a sure event.Therefore for any event $B$,
$P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{P(B)}{P(B)}=1$
Also,
$P(B \mid A)=\frac{P(A \cap B)}{P(A)}=\frac{P(B)}{1}=\frac{1}{2}$
Thus the correct pair is:
$P(A \mid B)=1$ and $P(B \mid A)=\frac{1}{2}$
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