Question 1111403
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.