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(A,) = 0.10 P(A, U Az) = 0.12 P(A, U A3) = 0.11 P(A2) = 0.08 P(A, U Az) = 0.12 P(A, n Az n Ag) = 0.01 P(A,) = 0.05 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) (b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)

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...
icon
Related questions
icon
Concept explainers
Topic Video
Question
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(A2) = 0.08
P(A, U A3) = 0.12
P(A, n A2 n A3) = 0.01
P(A,) = 0.10
P(A3) =
= 0.05
P(A, U A2)
= 0.12
P(A2 U A3) = 0.11
(a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.)
(b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.)
(c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.)
(d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four
decimal places.)
Transcribed Image Text: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(A2) = 0.08 P(A, U A3) = 0.12 P(A, n A2 n A3) = 0.01 P(A,) = 0.10 P(A3) = = 0.05 P(A, U A2) = 0.12 P(A2 U A3) = 0.11 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) (b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON