Machine A makes 15% of the components, machine makes 30%, machine C makes 35% and machine D makes the remainder. The probability that a board i acceptable is 0.93 when made by machine A, 0.96 when made by machine B, 0.95 when made by machine C and 0.93 when made by machine D. A board is picked at random Calculate the probability

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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8. Circuit boards are made by machines A, B, C and D.
Machine A makes 15% of the components, machine B
makes 30%, machine C makes 35% and machine D
makes the remainder. The probability that a board is
acceptable is 0.93 when made by machine A, 0.96
when made by machine B, 0.95 when made by
machine C and 0.93 when made by machine D. A
board is picked at random. Calculate the probability
that it is made by machine D and is unacceptable
O a.
0.1395
O b.
0.3325
O C.
0.014
O d. 0.012
Transcribed Image Text:8. Circuit boards are made by machines A, B, C and D. Machine A makes 15% of the components, machine B makes 30%, machine C makes 35% and machine D makes the remainder. The probability that a board is acceptable is 0.93 when made by machine A, 0.96 when made by machine B, 0.95 when made by machine C and 0.93 when made by machine D. A board is picked at random. Calculate the probability that it is made by machine D and is unacceptable O a. 0.1395 O b. 0.3325 O C. 0.014 O d. 0.012
Expert Solution
Step 1

Given:

P(A)=0.15P(B)=0.3P(C)=0.35P(D)=1-P(A)+P(B)+P(C)         =1-[0.15+0.30+0.35]         =0.2

P(Acceptable|A)=0.93P(Acceptable|B)=0.96P(Acceptable|C)=0.95P(Acceptable|D)=0.93 

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