A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A₁) = 0.15 P(A₂) = 0.11 P(A₁ U A₂) = 0.18 P(A₁ U A3) P(A₂ U A3) = 0.14 P(A₁ A₂ A3) = 0.02 (a) What is the probability that the system does not have a type 1 defect? P(A3) = 0.07 = 0.18 (b) What is the probability that the system has both type 1 and type 2 defects? (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?
A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A₁) = 0.15 P(A₂) = 0.11 P(A₁ U A₂) = 0.18 P(A₁ U A3) P(A₂ U A3) = 0.14 P(A₁ A₂ A3) = 0.02 (a) What is the probability that the system does not have a type 1 defect? P(A3) = 0.07 = 0.18 (b) What is the probability that the system has both type 1 and type 2 defects? (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?
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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Probability is the likelihood or chance of event happening. It takes the value between 0 to 1. The union of two events is calculated using the formula :
Here, is intersection of two events. Probability is calculated by dividing the favorable number of events and the total number of events.
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