If A and B be two events such that P(A)`=3/8,P(B)=5/8` and `P(AcupB)=3/4` then P(A/B).P(A'/B) is equal to

Options

A. `2/5`
B. `3/8`
C. `3/20`
D. `6/25`

Explanation

Here, `P(A)=3/8,P(B)=5/8andP(AcupB)=3/4`
`because P(AcupB)=P(A)+P(B)-P(AcapB)=3/4`
`becauseP(AcupB)=P(A)+P(B)-P(AcapB)`
`rArrP(AcapB)=3/8+5/8-3/4=(3+5-6)/8=2/8=1/4`
`becauseP(A//B)=(P(AcapB))/(P(B))=(1//4)/(5//8)=8/20=2/5`
and `P(A''//B)=(P(A'//B)=(P(A'capB))/(P(B))=(P(B)-P(AcapB))/(P(B))`
`=(5/8-1/4)/(5/8)=((5-2)/8)/(5/8)=3/5`
`therefore P(A//B)cdotP(A'//B)=2/5cdot3/5=6/25`