probability

[Var1995]

can someone solve this here? i have solved but need to confirm

[Amit Goyal]

Sample Space = {HH, HT, TH, TT}
Probability function satisfy: Pr({HH})=Pr({HT})=Pr({TH})=Pr({TT}) = 1/4
Note that
A = {HH, HT}
B = {HH, TH}
C = {HH, TT}

A and B are independent because Pr(A ∩ B) = Pr({HH}) = 1/4 = (1/2)(1/2) = Pr(A)Pr(B)
A and C are independent because Pr(A ∩ C) = Pr({HH}) = 1/4 = (1/2)(1/2) = Pr(A)Pr(C)
B and C are independent because Pr(B ∩ C) = Pr({HH}) = 1/4 = (1/2)(1/2) = Pr(B)Pr(C)

A, B and C are not independent because Pr(A ∩ B ∩ C) = Pr({HH}) = 1/4 ≠ 1/8 = (1/2)(1/2)(1/2) =Pr(A)Pr(B)Pr(C).

[Var1995]

thank you sir