Question 1041977
<img size=500 src = "http://textflow.mheducation.com/figures/1259299740/ch08-unfig42_lg.jpg">


There are 3 main branches. Each is equally likely to be chosen so each branch has a probability of 1/3.


There is only one main branch that leads directly to A. That is the middle main branch. The other 2 main branches break off to form sub-branches which some lead to A. The top main branch breaks up into 3 sub-branches. Each of those branches are equally possible, so 1/3*1/3 = 1/9 is the probability of going to each of those. 


Similarly, the same can be said for the bottom branch. However this branch only splits into 2 pieces (not 3) so each probability down here is 1/3*1/2 = 1/6


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So we have one main branch going to A. We have 2 sub-branches going to B. Adding up the probabilities gives


1/3 + 1/9+1/6 = 6/18 + 2/18 + 3/18 = (6+2+3)/18 = 11/18


The final answer is 11/18.