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

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Senior Manager
Joined: 02 Dec 2007
Posts: 449
The figure shown represents a board with 4 rows of pegs, and [#permalink]

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13 Sep 2008, 08:03
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Difficulty:

55% (hard)

Question Stats:

41% (01:45) correct 59% (00:51) wrong based on 37 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-figure-shown-represents-a-board-with-4-rows-of-pegs-and-36668.html
[Reveal] Spoiler: OA

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maths.doc [29.5 KiB]

Intern
Joined: 12 Feb 2010
Posts: 26
Re: The figure shown represents a board with 4 rows of pegs, and [#permalink]

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12 Feb 2010, 15:03
1/8 - 1/2*1/2*1/2.
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: The figure shown represents a board with 4 rows of pegs, and [#permalink]

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12 Feb 2010, 15:39
Attachment:

ps_539.jpg [ 9.74 KiB | Viewed 3064 times ]
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

When ball passes two pegs it will be either on the left route or on the right route. Now, if ball is on the left route, number of possible scenarios will be 4, out of which two will lead to cell 2, if ball is on the right route, number of scenarios will also be 4, but out of these four only one will lead to cell 2. So, total 8 scenarios out of which 2+1=3 lead to cell 2, hence probability 3/8.

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Re: The figure shown represents a board with 4 rows of pegs, and [#permalink]

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20 Apr 2015, 07:11
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Posts: 39673
Re: The figure shown represents a board with 4 rows of pegs, and [#permalink]

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20 Apr 2015, 08:14
OPEN DISCUSSION OF THIS QUESTION IS HERE: the-figure-shown-represents-a-board-with-4-rows-of-pegs-and-36668.html
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Re: The figure shown represents a board with 4 rows of pegs, and   [#permalink] 20 Apr 2015, 08:14
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