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Bunuel
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Upon arrival at Amari's Barber Shop, customers are randomly assigned 06 Feb 2023, 07:01
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D
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Difficulty:

35% (medium)

Question Stats:

66% (01:07) correct 34% (01:12) wrong based on 396 sessions

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Upon arrival at Amari's Barber Shop, customers are randomly assigned to one of three different chairs. If Bransen visits the barber shop on three separate occasions, what is the probability that he is assigned to a different chair in each visit ?

A. 1/27
B. 1/9
C. 1/6
D. 2/9
E. 1/3
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D
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ShowOff31
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Upon arrival at Amari's Barber Shop, customers are randomly assigned 06 Feb 2023, 09:01
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1st arrival - any seat
2nd - 2/3 available
3rd - 1/3 available
2/3 * 1/3 = 2/9
D
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peaky
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Upon arrival at Amari's Barber Shop, customers are randomly assigned 24 Jun 2025, 08:10
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Let instances be A,B,C

First visit let's choose A- 1/3
Second Visit B- 1/3
Third Visit C -1/3

We get 1/9

this can happen over 6 times

(1/9) * 6=0.667 2/9
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Upon arrival at Amari's Barber Shop, customers are randomly assigned 29 Jan 2026, 15:37
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Deconstructing the Question

Topic: Sequential Probability

Bransen visits the shop 3 times. There are 3 chairs available each time. We need the probability that he is assigned to a different chair in each visit.

1. Break down the visits
  • 1st Visit: He can sit in any of the 3 chairs.
    Probability = \(3/3 = 1\)
  • 2nd Visit: To be different from the first, he must sit in one of the 2 remaining chairs.
    Probability = \(2/3\)
  • 3rd Visit: To be different from the previous two, he must sit in the last remaining chair.
    Probability = \(1/3\)

2. Total Probability
Since these are independent sequential events, we multiply them:
\(P = 1 * (2/3) * (1/3) = \) 2/9

Alternative Method (Counting Outcomes):
* Total possible assignments: \(3 * 3 * 3 = 27\)
* Favorable outcomes (permutations of 3 chairs): \(3! = 3 * 2 * 1 = 6\)
* \(P = 6 / 27 = 2 / 9\)

The correct answer is D.
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