यदि `A` व `B` दो घटनाएँ इस प्रकार है कि `P(A)=(1)/(3),P(B)=(1)/(4)" और "P(AcapB)=(1)/(5)` हो, तो ज्ञात कीजिए-
`(i)` `P(A//B)` `(ii)` `P(B//A)`
`(iii)` `P(AcupB)` `(iv)` `P(barB//barA)`

Options

A. `(i) 4/5 , (ii) 3/5 , (iii) 23/5 , (iv) 37/5`
B. `(i) 4/5 , (ii) 3/5 , (iii) 23/60 , (iv) 37/5`
C. `(i) 4/5 , (ii) 3/5 , (iii) 23/5 , (iv) 37/40`
D. `(i) 4/5 , (ii) 3/5 , (iii) 23/60 , (iv) 37/40`

Answer

D

Explanation

(i) हम जानते है कि
`P(A//B)=(P(AcapB))/(A(B))=(1//5)/(1//4)=(4)/(5)`
(ii) `P(A//B)=(P(AcapB))/(P(A))=(1//5)/(1//3)=(3)/(5)`
(iii) `P(AcupB)=P(A)+P(B)-P(AcapB)`
`=((1)/(3)+(1)/(4)-(1)/(5))=(23)/(60)`
(iv) `P(barB//barA)=(P(barBcapbarA))/(P(barA))=(P(barAcapbarB))/(P(barA))`
`=(P(bar(AcupB)))/(P(barA))=(1-P(AcupB))/(1-P(A))`
`=((1-(23)/(60)))/((1-(1)/(3)))=(37)/(40)`