Question #f69b7

1 Answer
Daniel L.
Nov 27, 2017

The probability is about #9.9%#. See explanation.

Explanation:

The task requires to calculate the probability of incorrect conclusion. This means we have to calculate the probability that a defective device is detected as nondefective, or a nondefective device is detected defective.

The probabilities are as follows:

#P(D)=18/100#

#P(N)=82/100#

where:

#D# means that the part is defective,

#N# means part is non defective

After choosing the part it is checked.
The outcome can be:

#CD# - the part is classified as deffective

#CN# - the part is checked as non deffective

The probabilities are:

#P(CD//D)=95/100#

#P(CD//N)=11/100#

#P(CN//D)=5/100#

#P(CN//N)=89/100#

where

#CD//D# - means the defective part is checked as defective

#CD//N# - non defective part is checked as defective

#CN//D# - a defective part is checked as non defective

#CN//N# - a non defective part checked as defective

The false conclusion means that a defective part is detected as non defective or a non defective part is detected as defective.

The probability of false conclusion can be calculated as:

#P(F)=P(D)*P(ND//D)+P(N)*P(CD//N)=#

#18/100*5/100+82/100*11/100=90/10000+902/10000=#

#=992/10000=992/100%=9.92%~~9.9%#

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