conditional probablilty of A given B is the probability
of event A happening given that event B happens
you can see in a question when
conditional probability is used, when
it is says 'without replacement'
if events A and B are independent, then P(A
given B) = P(A) and P(B given A) = P(B)
if events A & B are dependent, then
P(A and B) = P(A) x P(B given A)
the probability of events A and B both happening is equal to
the probability of event A happening multiplied by the
probability of event B happening given that event A happens.
on tree diagrams, if you want one instance
you're investigating at the end, times the
probabilities in both the steps. if you need
probability of one option or another, than
add the probabilities of each