Question

. 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?

Answer 1

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%

Answer 2

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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