If ` E and F `are the complementary events of events `E and F ,` respectively, and if P(F) `in` [0,1]

Options

A. `P(E//F)+P(overline(E )//F)=1`
B. `P(E//F)+P(E//overline(F))=1`
C. `P(overline(E )//F)+P(E//overline(F))=1`
D. `P(E//overline(F))+P(overline(E )//overline(F))=1`

Answer

A, D

Explanation

Since `E//F " and " overline(E )//F` are complementary events.
`therefore P(E//F)+P(overline(E )//F)=1`
Similarly, `E// overline(F) " and " overline(E )// overline(F)` are also complementary events.
`therefore P(E// overline(F))+P(overline(E )// overline(F))=1`