Suppose P(A) = 0.7, P(B) = 0.6, P(C) = 0.2 and P(A ⋂ C) = 0.1. Suppose also that • A and C are conditionally independent given B, i.e., P(A⋂C|B) = P(A|B)P(C|B). • A and B are conditionally independent given C, i.e., P(A⋂B|C) = P(A|C)P(B|C). Compute P(A ⋂ B).

Suppose P(A) = 0.7, P(B) = 0.6, P(C) = 0.2 and P(A ⋂ C) = 0.1. Suppose also that • A and C are conditionally independent given B, i.e., P(A⋂C|B) = P(A|B)P(C|B). • A and B are conditionally independent given C, i.e., P(A⋂B|C) = P(A|C)P(B|C). Compute P(A ⋂ B).

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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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

Suppose P(A) = 0.7, P(B) = 0.6, P(C) = 0.2 and P(A ⋂ C) = 0.1. Suppose also that

• A and C are conditionally independent given B, i.e., P(A⋂C|B) = P(A|B)P(C|B).

• A and B are conditionally independent given C, i.e., P(A⋂B|C) = P(A|C)P(B|C).

Compute P(A ⋂ B).

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