10 marbles are in an urn, 4 are Red and 6 are Black. For randomly selecting three marbles without replacement, what is the probability all three are black?
Let's say A is an event where 1st one is black, B is an event 2nd one is black, C is an event 3rd one is black.
This is what I tried:
I understand how to solve this using the counting method, but I don't understand the step that I marked with the question mark in the picture. Can someone help me understand how we use multiplication rule when we have more than 2 events?
In order to understand the validity of the 2nd approach, you have to learn about Bayes Theorem which states that
given two events $R$ and $S$, with $p(RS)$ representing the probability of both events occurring, you have that
$p(S)p(R|S) = p(RS).$
Therefore, $p(A)p(B|A) = p(AB).$
Further, $p(AB)p(C|AB) = p(ABC).$