Question 1111403: It is known that of the articles produced by a factory, 20% come from Machine A, 30% from Machine B, and 50% from Machine C. The percentages of satisfactory articles among those produced are 95% for A, 85% for B and 90% for C. An article is chosen at random.
What is the probability that is satisfactory?
Assuming that the article is not satisfactory, what is the probability that it was produced by B?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let T equal the total numbert of articles produced.
the articles that come from A = .2T
the articles that come from B = .3T
the articles that come from C = .5T
you get .2T + .3T + .5T = T
95% of the articles produced by A are satisfactory.
85% of the articles produced by B are satisfactory.
90% of the articles produced by Care satisfactory.
.95A + .85B + .9C = S, where S equals the total satisfactory articles produced.
since A = .2T and B = .3T and C = .5T, then:
.95 * .2T + .85 * .3T + .9 * .5T = S
this gets you S = .895T.
this means 89.5% of all the articles produced are satisfactory.
if you let N equal the total number of articles that are not satisfactory, then:
S + N = T
solve for N to get N = T - S
since S = .895T, you get N = T - .895T which results in N = .105T
this means that 10.5% of all the articles produced are not satisfactory.
since 85% of the articles produced by B are satisfactory, then 15% of the articles produced by B are not satisfactory.
since B = .3T, you get .15 * .3T = .045T.
this means that, out of all the articles that are produced, .45% of them are unsatisfactory articles that come from B.
since, out of all the articles that are produced, 10.5% of them are not satisfactory, then the ratio of the unsatisfactory articles that are produced by B to the total number of unsatisfactory articles is .045/.105, which is equal to .4285714286.
that means that 42.85714286% of the articles that are unsatisfactory come from B.
answers to your questions should be:
An article is chosen at random.
1. What is the probability that is satisfactory?
the probability that it is satisfactory is .895, or 89.5%.
2. Assuming that the article is not satisfactory, what is the probability that it was produced by B?
assuming that the articles is not satisfactory, the probability that it came from B is .4285714286, or 42.85714286%
if you round the ratio to 4 decimal places, then the percent will be rounded to 2 decimal places.
you will get the ratio is .4286 and the percent is 42.86%.
round your answers as required.
i believe this is what you are looking for.
let me know if it's not.
|
|
|
