Question

Let Ω = {a, b, c, d, e, f}. Assume that m(a) = m(b) = 1/16 , and m(c) = m(d) = m(e) = m(f) = 7/32 . Let A, B and C be the events A = {a, d, e}, B = {a, c, e} and C = {a, c, d}. Are A, B, C mutually independent? Explain

Answer 1

here P(A)=P(a)+P(d)+P(e)=(1/16)+(7/32)+(7/32)=1/2

P(B)=P(a)+P(c)+P(e)=(1/16)+(7/32)+(7/32)=16/32=1/2

P(C)=1/2

P(A n B n C)=P(a)=1/16

here as P(A n B nC) is not equal to P(A)*P(B)*P(C)

therefore A, B and C are not  mutually independent.