SOLUTION: Is it D? I want to check my answer. The following shows a corn maze for participants to walk through. The participants can only go forward and when there is a fork in the path y

Algebra ->  Probability-and-statistics -> SOLUTION: Is it D? I want to check my answer. The following shows a corn maze for participants to walk through. The participants can only go forward and when there is a fork in the path y      Log On


   

Question 1161051: Is it D? I want to check my answer.
The following shows a corn maze for participants to walk through. The participants can only go forward and when there is a fork in the path you may assume that people are equally likely to take any one of the paths. It costs $5.00 to enter the maze and each participant gets $10.00 if they come out in a prize area.
Using a tree diagram or area model, determine the probability that a participant wins money.

A. 0.25
B. 0.50
C. 0.573
D. 0.472

The Venn diagram for the question and the question itself are provided in the link here: https://i.imgur.com/bc1utOr.png
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

You have the correct answer. Nice work.

Here is the original tree diagram. I redrew it to just focus on vertices (aka points) and edges (aka connecting lines). The other parts of the drawing such as the grass are just filler/distraction in my opinion.


For each decision branch or junction point, label the probabilities for the edges. The first junction has 3 choices, so assuming each path is equally likely we have probability 1/3 for each path. A similar situation happens with the other junctions.


Starting from each "cash" block on the right side, highlight out a path back to the starting point. This guarantees we win cash.

Whatever values are highlighted along the way are multiplied out. We can multiply the probabilities because the events of selecting any given path is independent from any other path selection.

Red path = (1/3)*(1/2)*(1/2) = 1/12
Red path,then blue path = (1/3)*(1/2) = 1/6
green path, then blue path = (1/3)*(1/2) = 1/6
purple path = (1/3)*(1/2)*(1/3) = 1/18
All of these paths describe a way to get a cash prize. Every other path leads to no cash prize.

Adding up those probabilities gives
1/12+1/6+1/6+1/18 = 3/36+6/36+6/36+2/36 = (3+6+6+2)/36 = 17/36

So the probability of winning a cash prize is 17/36 = 0.47222222222222
This rounds to 0.472