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28 Jun 2023, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (01:48) correct
62%
(01:42)
wrong
based on 151
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Randomly, six people A, B, C, D, E, and F sit around a circular table. What is the probability that A is in middle of B and F, B is in the middle of A and C, C is in the middle of B and D, D is in the middle of C and E, E is in the middle of D and F, F is in the middle of A and E?
A. 3/10
B. 1/10
C. 1/20
D. 1/60
E. 1/120
A. 3/10
B. 1/10
C. 1/20
D. 1/60
E. 1/120
28 Jun 2023, 09:24
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Bunuel
Answer: Option D
Please check the explanation as attachment
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Screenshot 2023-06-28 at 9.51.54 PM.png [ 1.06 MiB | Viewed 3253 times ]
28 Jun 2023, 09:41
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The probability that A is in the middle of B and F is 1/3, since A can sit in any of the 6 seats and there are 2 possible seats for each of B and F. Once A is seated, there are only 2 possible seats for B and F. The probability that B is in the middle of A and C is 1/2, since there are only 2 possible seats for C once A and B are seated. Similarly, the probability that C is in the middle of B and D is 1/2, the probability that D is in the middle of C and E is 1/2, the probability that E is in the middle of D and F is 1/2, and the probability that F is in the middle of A and E is 1/3. Therefore, the probability that all 6 conditions are satisfied is (1/3) x (1/2) x (1/2) x (1/2) x (1/2) x (1/3) = 1/60.
Answer is D.
Answer is D.
