Construct a contingency tree (like that in the attachment).

Identify those terminal nodes that correspond to the specified cases (the heavy lines in the attachment for this problem).

Multiply the branch probabilities together along the path leading to each terminal node corresponding to a specified case.

Finaly add up the terminal node probabilities to get:

(0.6x0.1x0.3)+(0.4x0.7x0.1)+(0.4x0.3x0.7).

RonL