If P(B)`=3/5,P(A//B)=1/2andP(AcupB)=4/5`, then `P(AcupB)'+P(A'cupB)` is equal to

Options

A. `1/5`
B. `4/5`
C. `1/2`
D. 1

Explanation

Here, `P(B)=3/5,P(A//B)=1/2`
and `P(AcupB)=4/5`
Since, `P(A//B)=(P(AcapB))/(P(B))`
`rArrP(AcapB)=P(A//B)cdotP(B)`
`=1/2xx3/5=3/10`
Also, `P(AcupB)=P(A)+P(B)-P(AcapB)`
`rArrP(A)=4/5-3/5+3/10=1/2`
`therefore P(AcupB)'=1-P(AcupB)=1-4/5=1/5`
and `P(A'cupB)=1-P(A-B)=1-P(AcapB')`
`=1-P(A)cdotP(B')`
`=1-1/2cdot2/5=4/5`
`rArr P(AcupB)'+P(A'cupB)=1/5+4/5=5/5=1`