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12 Nov 2018, 19:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
62% (02:55) correct
38%
(02:43)
wrong
based on 408
sessions
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The number of paths from one place to another place are as shown in the table below. A, B, C, D are four adjacent points in the given order. If Jack, who is at point A, wants to reach his destination, D. What is the probability that he does not pass through C?
- A. \(\frac{1}{4}\)
B. \(\frac{8}{27}\)
C. \(\frac{1}{3}\)
D. \(\frac{3}{7}\)
E. \(\frac{1}{2}\)
12 Nov 2018, 21:13
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EgmatQuantExpert
Hi,
This question is based on the concept of "the fundamental principle of counting".
Theory
If there are \(m\) ways to do one thing and \(n\) ways to do another thing, then the total number of ways to do both things is \(m \times n\) ways. This can be further generalized to any number of events. Here, we assume that all the choices are independent of one another.
Problem
Attachment:
E-Gmat_Path.png [ 32 KiB | Viewed 6689 times ]
Following paths are available from A to D:
- A-D = 1 path
A-B-D = 2*4 = 8 paths
A-C-D = 3*2 = 6 paths
A-B-C-D = 2*3*2 = 12 paths.
Total no. of paths = 1+8+6+12 = 27 paths. No. of paths without visiting point C = 1+8 = 9 paths.
Required probability = \(\frac{9}{27} = \frac{1}{3}\).
Answer (C).
Thanks.
General Discussion
14 Nov 2018, 05:15
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Solution
Given:
- • A, B, C, D are four places adjacent to each other
• Jack wants to go from A to D
• The number of different paths available between any two places are given in the table
To find:
- • The probability that he does not pass through C
Approach and Working:
- • Number of ways he can go from A – B – C - D = 2 * 3 * 2 = 12
• Number of ways he can go from A – B – D = 2 * 4 = 8
• Number of ways he can go from A – D = 1
• Number of ways he can go from A – C – D = 3 * 2 = 6
• Probability that he does not pass through C = \(\frac{[n(A – B – D) + n(A - D)]}{total number of ways to reach D} = \frac{(8 + 1)}{(12 + 8 + 1 + 6)} = \frac{9}{27} = \frac{1}{3}\)
Hence the correct answer is Option C.
Answer: C
