1. Four people are seated around a table as in the diagram below. Another clumsy personaccidentally spills water on two adjacent people at the table. (For example, the water couldbe spilled on 1 and 2, or on 1 and 4, but not on 1 and 3.) The clumsy person is equally likelyto spill water on any of the four adjacent pairs.2Let 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.

Given information: W1:Person 1 had water spilled on them.

Answered: Four people are seated around a table…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is five times as likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is four times as likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is twice as likely to have Chinese as Greek food the next week. Assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. Find the transition matrix for this Markov process. P = 出出曲

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30% of students take Physics101 and 20% take Math146. Of the students who take Physics 101, 25% also take Math146. The events taking Physics 101 and Math146 are O a. independent O b. dependent O c. Disjoint d. None of the above
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?
I need help on both questions. Thank you in advance!
question 10, 11 and 12 they are all multichoice please thank you !

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