If `P(A cap B)=1//3, P(A cup B)=5//6 " and " P(A)=1//2`, then which one of the following is correct ?

Options

A. A and B are independent events
B. A and B are mutually exclusive events
C. P(A)=P(B)
D. None of the above

Answer

A

Explanation

Given that, `P(AcapB)=(1)/(3)`
`P(AcupB)=(5)/(6)andP(A)=(1)/(2)`
`thereforeP(cupB)=P(A)+P(B)-P(AcapB)`
`implies(5)/(6)=(1)/(2)+P(B)-(1)/(3)`
`impliesP(B)=(5)/(6)+(1)/(3)-(1)/(2)=(4)/(6)=(2)/(3)`
`P(A)xxP(B)=(1)/(2)xx(2)/(3)=(1)/(3)=P(AcapB)`
This shows that A and B are independent events.