In a certain factory, machines A, B, and C are all producing widgets. Machines A
ID: 3355352 • Letter: I
Question
In a certain factory, machines A, B, and C are all producing widgets. Machines A, B, and C produce %, 4%, and 2% defective widgets, respectively. Of the total production of widgets in the factory, Machine A produces 30%, Machine B produces, 25%, and Machine C produces 45%. a.) If one widget is selected at random from the total produced on a given day, what is the probability it is defective? b.) Given that the widget is defective, what is the probability it was produced by machine A? c.) Given that the widget is not defective, what is the probability that it was produced by machine C?Explanation / Answer
A produces 30% with 1% defects
B produces 25% with 4% defects
C produces 45% with 2% defects
a.) Prob of 1 widget selected at random and it is defective = Sum product of defect and items = 30%*1% + 25%*4% + 45%*2% = 2.2% = 0.022
So., 2.2% is the probability of 1 widget selected at random and it is defective
b.) Given that the widgest is defective we need to find the prob that the m/c is defective = defective prob from m/c A/Total defctive widgets probability = 0.3*0.01 / 0.022 = 0.1363636
c.) Given that the widget is not defective we need to find the prob of it coming from m/c C = Widgets from m/c C which are non defective/total prob of non defective widgets = [0.45*(1-0.02)]/ (1-0.022) = 0.4509202
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