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An engineering firm uses one of five software companies to modify its products for its customers. Any piece of software can be modified with one and only one of these companies. Define the following events: S₁: the software was modified with company 1 S₂: the software was modified with company 2 S3: the software was modified with company 3 S4: the software was modified with company 4 ● S5: the software was modified with company 5 ● The engineering firm was found to use each of the software companies with the following probabilities: D(S) 0.50 D(S) 0.25 D(S) 0.05 DIS 010 DIS 010

An engineering firm uses one of five software companies to modify its products for its customers. Any piece of software can be modified with one and only one of these companies. Define the following events: S₁: the software was modified with company 1 S₂: the software was modified with company 2 S3: the software was modified with company 3 S4: the software was modified with company 4 ● S5: the software was modified with company 5 ● The engineering firm was found to use each of the software companies with the following probabilities: D(S) 0.50 D(S) 0.25 D(S) 0.05 DIS 010 DIS 010

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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An engineering firm uses one of five software companies to modify its products for its customers. Any piece of software can be modified with one and only one of these companies. Define the following events: ● ● S₁: the software was modified with company 1 S₂: the software was modified with company 2 S3: the software was modified with company 3 S4: the software was modified with company 4 S5: the software was modified with company 5 The engineering firm was found to use each of the software companies with the following probabilities: P(S₁) = 0.50 P(S₂) = 0.25 P(S3) = 0.05 P(S4) = 0.10 P(S5) = 0.10. Let X be the event that the software is modified successfully by the selected software company. Depending on the company chosen, the probability of X varies: P(X| S₁) = 0.95 P(X| S₂) = 0.75 P(X| S3) = 0.50 P(X| S4) = 0.65 P(X| S5) = 0.65 A. Compute the numerical value of P(S₁ U S2 U S3) B. Given that software has been modified successfully what is the probability that it was done with company S3? In other words, compute the numerical value of P(S3|X) – hint: use Bayes rule.
Transcribed Image Text:An engineering firm uses one of five software companies to modify its products for its customers. Any piece of software can be modified with one and only one of these companies. Define the following events: ● ● S₁: the software was modified with company 1 S₂: the software was modified with company 2 S3: the software was modified with company 3 S4: the software was modified with company 4 S5: the software was modified with company 5 The engineering firm was found to use each of the software companies with the following probabilities: P(S₁) = 0.50 P(S₂) = 0.25 P(S3) = 0.05 P(S4) = 0.10 P(S5) = 0.10. Let X be the event that the software is modified successfully by the selected software company. Depending on the company chosen, the probability of X varies: P(X| S₁) = 0.95 P(X| S₂) = 0.75 P(X| S3) = 0.50 P(X| S4) = 0.65 P(X| S5) = 0.65 A. Compute the numerical value of P(S₁ U S2 U S3) B. Given that software has been modified successfully what is the probability that it was done with company S3? In other words, compute the numerical value of P(S3|X) – hint: use Bayes rule.
Expert Solution
Step 1

An engineering firm uses one of five software companies to modify its products for its customers.

Any piece of software can be modified with one and only one of these companies. This means that modification of software by the companies is independent of one another.

Define the following events: 

S₁: the software was modified with company 1

S₂: the software was modified with company 2

S3: the software was modified with company 3

S4: the software was modified with company 4

S5: the software was modified with company 5 

 

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