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The figure shown represents a board with 4 rows of pegs, and

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The figure shown represents a board with 4 rows of pegs, and [#permalink] New post 06 Jan 2008, 09:57
The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has the probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end in Cell 2?


A. 1/16
B. 1/8
C. 1/4
D. 3/8
E. 1/2

see file attached.

I was frightened by the figure...so I didn't solve the question..anyway I believe it is only a question of how complex seems the figure...
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Re: probability [#permalink] New post 06 Jan 2008, 10:32
without looking at the picture my instinct is D. 3/8

if this is correct I'll try to explain it
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Re: probability [#permalink] New post 06 Jan 2008, 11:07
eschn3am wrote:
without looking at the picture my instinct is D. 3/8

if this is correct I'll try to explain it


yes, OA is D....what's your reasoning?
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Re: probability [#permalink] New post 06 Jan 2008, 11:56
marcodonzelli wrote:
eschn3am wrote:
without looking at the picture my instinct is D. 3/8

if this is correct I'll try to explain it


yes, OA is D....what's your reasoning?


First, picture one of these boards with the pegs in it. We've all seen them before, the ball bounces down from peg to peg until it lands in a slot at the bottom. Once you have this pictured, move on to the reasoning.

If each slot had an equal chance of having the ball land in it the odds would be 1/4 to 1/4 to 1/4 to 1/4 for each slot. All of the probabilities must equal up to 1 because the ball must land in one of the slots.

However, my thought process says that there isn't an equal chance of the ball landing in each of the slots. It is much more likely the ball would land in one of the more middle slots. Here's how it works:

For a ball to land in one of the far end slots (1 or 4) it would have to constantly be bouncing to the left of each peg (in the case of 1) or the right of each peg (in the case of 4) to end up on the far side of the slots. Now if it any point it takes a bounce in the opposite direction it's going to end up in one of the middle to slots. The middle slots aren't nearly as picky, as long as the ball doesn't bounce the same direction each time it'll wind up somewhere in the middle.

Now we know that the odds of the ball landing in 1 are the same as it landing in 4, and the odds of it landing in 2 are the same as 3. So we're looking for a number that is greater than 1/4, but when doubled still leaves room for the odds of 1 and 4.

3/8 is the only answer that makes sense

3/8 for 2
3/8 for 3
6/8 it'll land somewhere in the middle, leaving 2/8 it'll land in either of the extreme slots (1 or 4)

none of the other options work!

Now you could spend a lot more time trying to decipher that horrible drawing and come up with a formula, but why bother? using a little logic and imagination you can come to the correct answer in no time at all
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Re: probability [#permalink] New post 06 Jan 2008, 12:13
eschn3am wrote:
marcodonzelli wrote:
eschn3am wrote:
without looking at the picture my instinct is D. 3/8

if this is correct I'll try to explain it


yes, OA is D....what's your reasoning?


First, picture one of these boards with the pegs in it. We've all seen them before, the ball bounces down from peg to peg until it lands in a slot at the bottom. Once you have this pictured, move on to the reasoning.

If each slot had an equal chance of having the ball land in it the odds would be 1/4 to 1/4 to 1/4 to 1/4 for each slot. All of the probabilities must equal up to 1 because the ball must land in one of the slots.

However, my thought process says that there isn't an equal chance of the ball landing in each of the slots. It is much more likely the ball would land in one of the more middle slots. Here's how it works:

For a ball to land in one of the far end slots (1 or 4) it would have to constantly be bouncing to the left of each peg (in the case of 1) or the right of each peg (in the case of 4) to end up on the far side of the slots. Now if it any point it takes a bounce in the opposite direction it's going to end up in one of the middle to slots. The middle slots aren't nearly as picky, as long as the ball doesn't bounce the same direction each time it'll wind up somewhere in the middle.

Now we know that the odds of the ball landing in 1 are the same as it landing in 4, and the odds of it landing in 2 are the same as 3. So we're looking for a number that is greater than 1/4, but when doubled still leaves room for the odds of 1 and 4.

3/8 is the only answer that makes sense

3/8 for 2
3/8 for 3
6/8 it'll land somewhere in the middle, leaving 2/8 it'll land in either of the extreme slots (1 or 4)

none of the other options work!

Now you could spend a lot more time trying to decipher that horrible drawing and come up with a formula, but why bother? using a little logic and imagination you can come to the correct answer in no time at all


Oh, yeah!!! This is what a call parallel thinking. This is the typical question in which you have to do so many calculations that you have to find a shorter way to answer it. And for counting-probability questions it works many times.
Re: probability   [#permalink] 06 Jan 2008, 12:13
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