Four people are seated around a table as in the diagram below. Another clumsy person accidentally spills water on two adjacent people at the table. (For example, the water could be spilled on 1 and 2, or on 1 and 4, but not on 1 and 3.) The clumsy person is equally likely to spill water on any of the four adjacent pairs. 4 2 Let W₁ be the event "person 1 had water spilled on them". Define W2, W3, W4 similarly. (a) Which pairs of the events W₁, W2, W3, W₁ are independent? Explain why. (b) Which pairs of the events W₁, W2, W3, W4 are disjoint? Explain why.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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1. Four people are seated around a table as in the diagram below. Another clumsy person
accidentally spills water on two adjacent people at the table. (For example, the water could
be spilled on 1 and 2, or on 1 and 4, but not on 1 and 3.) The clumsy person is equally likely
to spill water on any of the four adjacent pairs.
2
Let W₁ be the event "person 1 had water spilled on them". Define W2, W3, W4 similarly.
(a) Which pairs of the events W₁, W2, W3, W₁ are independent? Explain why.
(b) Which pairs of the events W₁, W2, W3, W4 are disjoint? Explain why.
Transcribed Image Text:1. Four people are seated around a table as in the diagram below. Another clumsy person accidentally spills water on two adjacent people at the table. (For example, the water could be spilled on 1 and 2, or on 1 and 4, but not on 1 and 3.) The clumsy person is equally likely to spill water on any of the four adjacent pairs. 2 Let W₁ be the event "person 1 had water spilled on them". Define W2, W3, W4 similarly. (a) Which pairs of the events W₁, W2, W3, W₁ are independent? Explain why. (b) Which pairs of the events W₁, W2, W3, W4 are disjoint? Explain why.
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