Question

If P(a|b,c) = P(a) then prove that P(b|c) = P(b). Can anyone give a step by step explanation to prove this?

Answer 1

Not true

Answer 2

Ok..could you please elaborate your answer?

Answer 3

Or better if you can give some counter example..I would really appreciate that.

Answer 4

roll a die and flip a coin

let A={roll a 2}
B=head
C=tail

then P(A|B,C)=P(A)

since A is independent of B and C

but P(B|C)=0\(\neq\frac{1}{2}\)=P(B)