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Gmat prep problem - Expert's help preferred

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by GMATGuruNY » Thu Mar 08, 2012 2:13 pm
Each time the ball descends a level, it has 2 options: to fall TO THE LEFT or TO THE RIGHT.
Since the ball descends 3 levels, and there are 2 options for each level, the total number of routes = 2*2*2 = 8.
There is only 1 way to land in slot 1 (straight down the left side of the triangle) and only 1 way to land in slot 4 (straight down the right side of the triangle).
Each of the 6 remaining routes leads to the one of the two middle slots.
Since the probability of landing in either of the two middle slots is the same, 3 of these 6 remaining routes lead to slot 2.
Thus, P(slot 2) = 3/8.

The correct answer is D.
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by winniethepooh » Thu Mar 08, 2012 2:59 pm
Thanks Mitch. I should directly Pm you when I need exceptional solutions!
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by ranjeet75 » Fri Mar 09, 2012 7:54 am
[quote="GMATGuruNY"]Each time the ball descends a level, it has 2 options: to fall TO THE LEFT or TO THE RIGHT.
Since the ball descends 3 levels, and there are 2 options for each level, the total number of routes = 2*2*2 = 8.
[color=red]There is only 1 way to land in slot 1 (straight down the left side of the triangle) and only 1 way to land in slot 4 (straight down the right side of the triangle).
Each of the 6 remaining routes leads to the one of the two middle slots.[/color]
Since the probability of landing in either of the two middle slots is the same, 3 of these 6 remaining routes lead to slot 2.
Thus, P(slot 2) = 3/8.

The correct answer is [spoiler]D[/spoiler].[/quote]


Please explain the red coloured portion as I could not understand it.
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by [email protected] » Wed Mar 14, 2012 8:04 pm
Such a simple explanation could only be possible for Mitch.Thanks!
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by sam2304 » Wed Mar 14, 2012 11:15 pm
There is only 1 way to land in slot 1 (straight down the left side of the triangle) and only 1 way to land in slot 4 (straight down the right side of the triangle).
Each of the 6 remaining routes leads to the one of the two middle slots.

Please explain the red coloured portion as I could not understand it.
To hit cell numbered 1, the ball has to come all the way left, if it goes right anywhere in the middle it won't hit cell 1. So there is only 1 way. [see the picture if you don't understand it] Similar manner to hit 4 it has to go all the way right - one way. Total 8 ways, one for cell 1, one for cell 4 and remaining 6 for cell 2 and 3.
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