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,) = 0.15P(A, U A2) = 0.16P(A2 U A3) = 0.12P(A2) = 0.09P(A, U A3) = 0.17P(A, n A2 n A3) = 0.02P(A,) = 0.06.(a).What.is.the probability that the system does not have a type 1 defect?Enter a number.(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?(d) What is the probability that the system has at most two of these defects?

Answered: A certain system can experience three…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

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(A,) = 0.15
P(A, U A2) = 0.16
P(A2 U A3) = 0.12
P(A2) = 0.09
P(A, U A3) = 0.17
P(A, n A2 n A3) = 0.02
P(A,) = 0.06
.(a).What.is.the probability that the system does not have a type 1 defect?
Enter a number.
(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?
(d) What is the probability that the system has at most two of these defects?

Expert Solution

Step 1

Since you have posted a question with multiple sub-parts, we will solve the first three subparts for you. To get the remaining sub-parts solved, please repost the complete question and mention the sub-parts to be solved.

In the provided information, it can be interpreted that the probability types of the defects, i.e., type-1, type-2, and type-3 are denoted by, P(A₁), P(A₂), and P(A₃). Furthermore, it can be claimed that the events, i.e., the type-1, type-2, and type-3 defects are not disjoint.