Suppose we have three events A, B and C such that A and B are conditionally indepen-dent given either C or Cº. The following probabilities are kmown:• P(C) = 0.15.• P(A|C) = 0.3, P(B|C) = 0.2.P(A|C) = 0.6, P(B|C°) = 0.4.Answer the following questions:(a) Show whether A and B are independent or not.Calculate(b) P(AU B¶C).

A and B are conditionally independent given either C of Cc . Therefore, P(A∩B|C) = P(A|C) P(B|C)…

Answered: Suppose we have three events A, B and C…

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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. Initial diagnosis of a patient’s illness was potentially flu (F), cold (C), or hay fever (H), with probabilities 0.1, 0.2, and 0.7 respectively. A lab test was then taken from the patient. Past tests on similar patients show the following conditional probabilities on the test result being positive (+), neutral (0), or negative (-):•P(+|F) = 0.7P(0|F) = 0.2P(-|F) = 0.1•P(+|C) = 0.1P(0|C) = 0.8P(-|C) = 0.1•P(+|H) = 0.1P(0|H) = 0.2P(-|H) = 0.7•Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or – test result has been observed.
. An electronic assembly consists of two subsystems A and B. The following probabilities are known. P(A fails) = 0.25, P( A and B fail) = 0.14 and P(B fails alone) = 0.15. Evaluate P (A fails alone) P (A fails given that B has failed) (Explain the solution using Venn diagram)
Q. 2 A car dealer notes the following probabilities about his customers: P(those who buy a new car ) = 0.25 P(those who buy a European car) = 0.30 P(those who neither buy a new car nor an European car ) = 0.58 Find the probability that next customer buys a new European car?
Suppose we have events A, B, and C with probabilities: P ( A ) = 0.4 , P ( B ) = 0.2 , P ( C ) = 0.3. We also know that: A and B are independent, A and C are mutually exclusive, and P ( B ∩ C ) = 0.15 Compute each of the following. Write your answers as decimals. P ( A ∩ B ) = P ( A ∪ B ) = P ( B ∪ C ′ ) =
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A restaurant owner wanted to know which time range are popular among the customers. Data were collected on the following events: L = a customer usually visits the restaurant during lunch time D = a customer usually visits the restaurant during dinner time Data collected suggest the following: P( L ) = 0.6 P( D ) = 0.7 P( L and D) = 0.3 What is the possibility that a customer only visit the restaurant during dinner time
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Q-3 If P(A) = 0.2, P(B) = 0.3, and P(A n B) = 0.1, determine the following probabilities: b. P(A U B) с. Р(А' n B) a. P(A' U B) d. P(A n B') e. P[(A U B)]
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