Question

if C and D are independent

are C^c and D^c independent

Answer 1

yes

Answer 2

so are C^c and D


also

C and D^c

Answer 3

no...you can prove it

Answer 4

let me use ' for complement


P(C',D')=1-P(C or D)
=1-P(C)-P(D)+P(C,D)
=1-P(C)-P(D)+P(C)P(D)
=1-P(C)-P(D)(1-P(C))
=(1-P(C))(1-P(D))
=P(C')P(D')


hence they are independent

Answer 5

thanks

Answer 6

no problem