Let `Aa n dB` b e two independent events. Statement 1: If `(A)=0. 3a n dP(Auu barB )=0. 8 ,t h e nP(B)` is 2/7. Statement 2: `P(barE)=1-P(E),w h e r eE` is any event.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

D

Explanation

Clearly, statement-2 is true.
If A and B are independent events such that
`P(A cup overline(B))=0.8`
`implies 1-P(overline(A))P(overline(B))=0.8`
`implies 1-(1-P(A))P(B)=0.8`
`implies 1-0.7P(B)=0.8 implies P(B)=(2)/(7)`
So, statement-1 is true and statement-2 is a correct explanation for statement-1.