SOLUTION: Assuming that at each branch point in the maze below any branch is equally likely to be chosen, determine the probability of entering room A. (Type an integer or a simplified fract

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Question 1041977: Assuming that at each branch point in the maze below any branch is equally likely to be chosen, determine the probability of entering room A. (Type an integer or a simplified fraction.)
Picture below is of the maze
http://textflow.mheducation.com/figures/1259299740/ch08-unfig42_lg.jpg
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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.