Let A and B be independent events aAre Ac and Bc independent

Let A and B be independent events. a)Are A^c and B^c independent? Prove your answer
-b)If A is independent of C and B is independent of C, and A B is independent of C, show that A B is independent of C
c). Let S be the entire probability space, are S and independent? Prove.

Solution

a)

they will be independen if P(A)*P(B) = P(A and B)

-b)If A is independent of C and B is independent of C, and A B is independent of C, show that A B is independent of C

A u B will be indpeendt of C because A and B is indepndent of C

c). Let S be the entire probability space, are S and independent? Prove.

No, they are mutually exclusive , but not indpendent