If P(A) = 2/3 , P(B) = 1/2 and {rm{ }}P(A cup B) = 5/6 then events A and B are

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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.

Standard 11

Mathematics

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