Question

If A and B are two events such that P(AUB) = 5/6, P(AĒB)

= 1/3, P( $\overline { \mathrm { B } }$ ) = ½, then the events A and B are

• A. Dependent
• B. Independent
• C. Mutually exclusive
• D. None of these

Answer 1

Answer: (B)

Independent

Answer 2

P(2) = 1 – P ( $\overline { \mathrm { B } }$ ) = 1 - $\frac { 1 } { 2 } = \frac { 1 } { 2 }$

and P(AUB) = P(1) + P(2) – P(AĒB)

or, $\frac { 5 } { 6 } = \mathrm { P } ( \mathrm { A } ) + \frac { 1 } { 2 } - \frac { 1 } { 3 }$

Ž P(1) = $\frac { 2 } { 3 }$

\ P(1) P(2) =

Hence, A and B are independent.