show that if the conditional probabilities exist then $$p(A_1\cap A_2 \cap \cdots \cap A_n) = p(A_1)p(A_2\mid A_1)p(A_3\mid A_1\cap A_2)\cdots p(A_n\mid A_1\cap A_2 \cap A_3\cap\cdots\cap A_{n-1})$$
I am lost, because if this is what i am given what do they want e to do? Perhaps show an induction proof for the $n+1$ case?
The definition given of conditional probability is the usual $p(A\cap B) = p(A\mid B)p(B)$
Best Answer
Yes, I think your thought is correct. They want to see an inductive proof using the definition of conditional probability.