Tree diagram

Branches at the first stage carry the probabilities of the starting events, and branches further out carry conditional probabilities given the path so far. Multiplying along a path is just the general multiplication rule $P(A \cap B) = P(A) \cdot P(B \mid A)$ drawn in picture form. From a bag of 3 red and 2 blue chips, drawing two without replacement gives $P(\text{red then blue}) = \frac{3}{5} \cdot \frac{2}{4} = 0.3$. To get the probability of a result that several paths lead to, add those path probabilities.