A Bayesian network has four variables: C,S,R,W, where -- C is independent, with P(C)=0.5 -- S is conditional on C, with P(S|C)=0.1, and P(S|~C)=0.5 -- R is conditional on C, with P(R|C)=0.8, and P(R|~C)=0.2 -- W is conditional on S and R, with P(W|S,R)=0.99, P(W|S,~R)=0.9, P(W|~S,R)=0.9,P(W|~S,~R)=0. a) List possible states of this world. b) Calculate the probability P(R|S).

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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Concept explainers

Use of XOR function

XOR function or exclusive OR function was introduced in Excel 2013. This function is available under excel logical functions. For the given statement, the XOR function will return true only when either of the statements is true. It returns false when both the statements are true or when both the statements are false.

Question

A Bayesian network has four variables: C,S,R,W, where

-- C is independent, with P(C)=0.5

-- S is conditional on C, with P(S|C)=0.1, and P(S|~C)=0.5

-- R is conditional on C, with P(R|C)=0.8, and P(R|~C)=0.2

-- W is conditional on S and R, with P(W|S,R)=0.99, P(W|S,~R)=0.9, P(W|~S,R)=0.9,P(W|~S,~R)=0.

a) List possible states of this world.
b) Calculate the probability P(R|S).

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