Gujarati
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

Similar Questions