Lypes of the following probabilities are true. P(A,) = 0.15 P(A, U A2) = 0.17 P(A, U A3) = 0.15 P(A,) = 0.10 P(A, U A3) = 0.18 P(A, N A, NAg) = 0.02 P(A,) = 0.08 (a) What is the probability that the system does not have a type 1 defect? 0.85 (b) What is the probability that the system has both type 1 and type 2 defects? 0.08 (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? 0.06 (d) What is the probability that the system has at most two of these defects?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 83CR
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I need assistence with part D

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) = 0.17
P(A, U A3) = 0.15
P(A,) = 0.10
P(A, U A3) = 0.18
P(A, N A, N A) = 0.02
P(A,) = 0.08
(a) What is the probability that the system does not have a type 1 defect?
0.85
(b) What is the probability that the system has both type 1 and type 2 defects?
0.08
(c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?
0.06
(d) What is the probability that the system has at most two of these defects?
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(A,) = 0.15 P(A, U A2) = 0.17 P(A, U A3) = 0.15 P(A,) = 0.10 P(A, U A3) = 0.18 P(A, N A, N A) = 0.02 P(A,) = 0.08 (a) What is the probability that the system does not have a type 1 defect? 0.85 (b) What is the probability that the system has both type 1 and type 2 defects? 0.08 (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? 0.06 (d) What is the probability that the system has at most two of these defects?
Expert Solution
Step 1

Given that 

Let Ai (i=1,2,3) denote the event that the system has a defect of type i 

P(A1)=0.15 , 

P(A2)=0.10

P(A3)=0.08

P(A1A2A3)=0.02

P(A1UA2)=0.17

P(A2UA3)=0.18

P(A2UA3)=0.15

We have to find the probability that the system has at most two of these defects 

 

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