FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 9.1324
100 24 6 0.857
24 4 28 7
100 100
= = = =
+
Example 17 :
A company has two plants to manufacture scooters. Plant I manufactures 80% of the scooters and plant II
manufactures 20%. At Plant I, 85 out of 100 scooters are rated standard quality or better. At Plant II, only 65
out of 100 scooters are rated standard quality or better. What is the probability that the scooter selected at
random came from Plant I if it is known that the scooter is of standard quality?
What is the probability that the scooter came from Plant II if it is known that the scooter is of standard
quality.
Solution :
Let A 1 be the event of drawing a scooter produced by Plant I and A 2 be the event of drawing a scooter
produced by Plant II. B be the event of drawing a standard quality scooter produced by either PlantI or
Plant II
Then, from the first information :
1
2P(A )^80 80% 0.80
100
P(A )^20 20% 0.2
100
= = =
= = =
From the additional information :
1 2P(B|A )^85 85%; P (B|A ) 65%
= 100 = =
The required values are computed in the following table :
Event Prior Conditional Joint Posterior Probability
Probability(2) Probability(3) Probability (4) (Revised)(5) [4÷ P(B)]A 1 0.80 0.85 0.68 0.68 680.81 81=A 2 0.20 0.65 0.13 0.13 130.81 81=
1 P(B) = 0.81 1From the first information we may say that the standard scooter is drawn from Plant I since P(A 1 ) = 80%
which is greater than P(A 2 ) = 20%,
From the additional information i.e. at Plant I, 85 out of 100 and at Plant II 65 out of 100 are rated standard
quality, we can give better answer, Thus we may conclude that the standard quality of scooter is more
likely drawn from the output by Plant I.