Question

If $P ( A ) = 2 / 3$ , $P ( B ) = 1 / 2$ and $P ( A \cup B ) = 5 / 6$ then events A and B are

• A. Mutually exclusive
• B. Independent as well as mutually exhaustive
• C. Independent
• D. Dependent only on A

Answer 1

Answer: (A)

Mutually exclusive

Answer 2

$P ( A \cup B ) = P ( A ) + P ( B ) - P ( A \cap B )$

$\frac { 5 } { 6 } = \frac { 2 } { 3 } + \frac { 1 } { 2 } - P ( A \cap B )$ $\Rightarrow P ( A \cap B ) = 0$

∴ Events A and B are mutually exclusive.