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

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by BTGmoderatorLU » Tue Feb 19, 2019 3:16 pm

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B

C

D

E

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Source: GMAT Prep

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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 showed 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

The OA is D
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by Jay@ManhattanReview » Tue Feb 19, 2019 9:40 pm
BTGmoderatorLU wrote:Source: GMAT Prep

Image

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 showed 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

The OA is D
So, there are three ways by which the ball can go in Cell 2. If the ball goes...

1. Left --> Left --> Right; probability = 1/2*1/2*1/2 = 1/8;
2. Left --> Right --> Right; probability = 1/2*1/2*1/2 = 1/8;
3. Right --> Left --> Left; probability = 1/2*1/2*1/2 = 1/8

Total probability = 1/8 + 1/8 + 1/8 = 3/8

The correct answer: D

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Fri Feb 22, 2019 3:16 pm
BTGmoderatorLU wrote:Source: GMAT Prep

Image

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 showed 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

The OA is D
Let L denote the event that the ball hits a peg and passes through the left opening and R denotes the event that the ball hits a peg and passes through the right opening. The routes that end at the second bin are L - L - R, L - R - L and R - L - L. Notice that each of these routes have a probability of 1/2 x 1/2 x 1/2 = 1/8 and since there are three such routes, the overall probability that the ball ends up in the second bin is 3 x 1/8 = 3/8.

Answer: D

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