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

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The figure shown represents a board with 4 rows of pegs, and at the bo [#permalink] New post   09 Mar 2022, 09:07
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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

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D
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GeminiHeat
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Re: The figure shown represents a board with 4 rows of pegs, and at the bo [#permalink] New post   10 Mar 2022, 10:45
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There are 4 rows.

the ball has 2 ways of moving-- to left or to right..
again when it falls in the peg in lower row, it can move to either direction- left or right ..
the final row again can have two ways

so TOTAL ways = 2*2*2 = 8 ways..

now ways the ball will fall in 1 = ways it will fall in 4..
and ways the ball will fall in 2 = ways it will fall in 3..

If you look at ways it can go in 1-
at every PEG, the ball has to move ONLY to left, so ways = 1*1*1 = 1 way

similarly in 4, the ball has to move ONLY to RIGHT so 1 way..

total ways for 3 and 2 = 8-2=6..
ways for each = 6/2 = 3..
prob of ball falling in 2 = 3/8

Answer: D
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gmatclubot
Re: The figure shown represents a board with 4 rows of pegs, and at the bo [#permalink]
10 Mar 2022, 10:45
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