Answer to Question #39605 in Statistics and Probability for sam

Question

Hi i just wanted to check whether this mathematical formula is correct for my problem description.
With Probability a event X will happen and with probability (1-a) event Y will happen. Event Y in its own turn can be divided to two subevent Y1(with probability b) and Y2(with probability 1-b). Therefore I am wondering can i write the whole problem of a * (x) + (1-a) (y) to sth like .....> a *(x) + (b * (y1) + (1-b) * (y2))