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1) The probabilities of poor print quality given “no printer problem”, “misaligned paper”, “high ink viscosity”, or “printer-head debris” are 0, 0.3, 0.4, and 0.6 respectively. The probabilities of “no printer problem”, “misaligned paper”, “high ink viscosity”, or “printer-head debris” are 0.7, 0.05, 0.15 and 0.1, respectively. (a) Determine the probability of “high ink viscosity” given poor print quality (b) Given poor print quality, what problem is most likely?

1) The probabilities of poor print quality given “no printer problem”, “misaligned paper”, “high ink viscosity”, or “printer-head debris” are 0, 0.3, 0.4, and 0.6 respectively. The probabilities of “no printer problem”, “misaligned paper”, “high ink viscosity”, or “printer-head debris” are 0.7, 0.05, 0.15 and 0.1, respectively. (a) Determine the probability of “high ink viscosity” given poor print quality (b) Given poor print quality, what problem is most likely?

Calculus For The Life Sciences
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
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 15E
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1) The probabilities of poor print quality given “no printer problem”, “misaligned paper”, “high ink viscosity”, or “printer-head debris” are 0, 0.3, 0.4, and 0.6 respectively. The probabilities of “no printer problem”, “misaligned paper”, “high ink viscosity”, or “printer-head debris” are 0.7, 0.05, 0.15 and 0.1, respectively. (a) Determine the probability of “high ink viscosity” given poor print quality (b) Given poor print quality, what problem is most likely?
Expert Solution
Step 1

Given that,

The events are as follows,

The event A is no print problem

The event B is misaligned paper

The event C is high ink viscosity

The event D is printer-head debris

The event E is the poor print quality

P(A)=0.7P(B)=0.05P(C)=0.15P(D)=0.1

The conditional probabilities are

P(E|A)=0P(E|B)=0.3P(E|C)=0.4P(E|D)=0.6

The Bayes theorem formula is 

P(A|B)=P(B|A)P(A)P(B)

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