. A company produces batteries. On average, 85% of all batteries produced are good. Each
battery is tested before being dispatched, and the inspector correctly classifies the battery 90%
of the time.
A. What percentage of the batteries will be “classified as good”?
B. What is the probability that a battery is defective given that it was classified as good?
Answers
Given :
Batteries produced = 85%
Batteries classified correctly = 90%
To find :
Percentage of the batteries classified as good ?
Probability that a battery is defective given that it was classified as good?
Solution:
Good Batteries = 85 %
Batteries which are not good = 100 - 85% = 15%
Correct classification = 90%
Incorrect classification = 100 - 90% = 10%
Good batteries out of 85 % good
= (90/100) × 85 %
= 76.5 %
Batteries that are not good out of 85% good
= (10/100) × 85 %
= 8.5%
Classified batteries good out of 15 % not good
= (10/100) × 15 %
= 1.5%
Classified batteries that are not good out of 15 %
= (90/100) × 15%
= 13.5%
Percentage of batteries classified as good
= 76.5 + 1.5 = 78%
Classified goods and actual goods = 76.5%
Classified good and defectives = 1.5%
Probability battery is defective, then it was classified as good
= (1.5)/(1.5 + 76.5)
= 1.5/78
= 1/52
= 1.92 %
Answer: Probability a battery is defective, given that it was classified as good is 1.92%
Given : A company produces batteries. On average, 85% of all batteries produced are good. Each battery is tested before being dispatched, and the inspector correctly classifies the battery 90% of the time.
To find : A. What percentage of the batteries will be “classified as good”?
B. What is the probability that a battery is defective given that it was classified as good?
Solution:
Good Batteries = 85 %
Not good Batteries = 100 - 85 % = 15 %
inspector correctly classifies the battery 90% of the time.
=> 100 - 90 % = 10 % is incorrect classification
Classified Good batteries out of 85 % good = (90/100) 85 % = 76.5 %
Classified not good Batteries out of 85 % good = (10/100) 85 % = 8.5 %
Classified not Good batteries out of 15 % not good = (90/100) 15 % = 13.5 %
Classified Good Batteries out of 15 % not good = (10/100) 15 % = 1.5 %
percentage of the batteries classified as good = 76.5 + 1.5 = 78 %
Classified good and actual good = 76.5 %
Classified Good and actual not good ( defective) = 1.5 %
probability that a battery is defective given that it was classified as good
= (1.5)/(1.5 + 76.5)
= 1.5/78
= 1/52
= 1.92 %
78 % of the batteries will be “classified as good"
probability that a battery is defective given that it was classified as good = 1.92 %
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