probability in the paint factory.?

Question

in the four weeks of dec 2011. seven thousand gallons of paint were sold and yesterday a total of 123 gallons were sent back by the distributor as "spoiled", 113 of them were checked as emulsifier error and 10 as color failure. The production can be grouped by colors as follows: 1345 yellow; 2746 blue; 2332 red and 577 white. a) What is the probability that a gallon of white paint be spoiled. 
b)And if a blue gallon is spoiled, what is the probability it is by emulsifier error.

Polygon · Accepted Answer

Pr. of spoilage = 123/7000 = 0.0176  >>>>> Pr (emulsifier) = 113/123 =  0.919
                                                                       Pr Color failure) = 10/123 = 0.081
                                                                                                                 -----------
                                                                                                                    1.000
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Pr. (yellow) = 1345/7000  =  0.192
Pr. (blue)    = 2746/7000  =  0.393
Pr. (red)    = 2332/7000    =  0.333
Pr.(white)  = 577/7000      =  0.082
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Pr Emulsifier

                                             ---------
                                              1.000
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Pr(emulsifier|+yellow)  0.919*0.192  = 0.176
Pr(emulsifier +Blue)     0.919*0.393  = 0.358
Pr (emulsifier + red)     0.919*0.333  = 0.306
Pr (emulsifier(white)     0.919* 0.082  = 0.075

Pr (color+ yellow)   = 0.031*0.192   = 0.006
Pr (color + blue)     = 0.031* 0.393  = 0.012
Pr. (Color + red)     = 0.031*0.333   = 0.010
Pr. (color + white)   = 0.031*0.082  = 0.003

Pr of white being spoiled = Pr(emulsifier + white) + Pr. Color + white) =0.078 
Pr of emulsifier + blue = 0.358

probability in the paint factory.?

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