Two events A and B will be independent, if(A) A and B are mutually exclusive(B) `P(Aprime ∩ Bprime)=[1-P(A)][1-P(B)]`(C) `P(A) = P(B)` (D) `P(A) + P(B) = 1`

Options

A. A and B are mutually exclusive
B. `P(A'B')=[1-P(A)][1-P(B)]`
C. `P(A)=P(B)`
D. `P(A)+P(B)=1`

Answer

A

Explanation

(b)
Events A and B are independent if
`P(AnnB)=P(A)P(B)`
`:.P(A'nnB')=P(AnnB)'=P(AuuB)'=1-P(AuuB)`
`=1-[P(A)+P(B)-P(AnnB)]`
`[ :'P(AuuB)'=1-P(AuuB)]`
`=1-P(A)-P(B)+P(A)P(B)`
`=[1-P(A)][1-(B)]`