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14.Probability
easy
If $P(A) = 2/3$, $P(B) = 1/2$ and ${\rm{ }}P(A \cup B) = 5/6$ then events $A$ and $B$ are
A
Mutually exclusive
B
Independent as well as mutually exhaustive
C
Independent
D
Dependent only on $A$
Solution
(a) $P(A \cup B) = \,P(A) + P(B) – P(A \cap B)$
$\frac{5}{6} = \frac{2}{3} + \frac{1}{2} – P(A \cap B)$
$ \Rightarrow \,P(A \cap \,B) = 0$
$\therefore$ Events $A$ and $B$ are mutually exclusive.
Std 11
Mathematics
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