A subassembly is made up of three components A, B, and C. A large batch of these

Question

A subassembly is made up of three components A, B, and C. A large batch of these units are supplied to the production site and the proportion of defective units in these is 5% of the component A, 10% of the component B, and 4% of the component C. [5 Marks] (a) What proportion of the finished subassemblies will contain no defective components? (b) What proportion of the finished subassemblies will contain exactly one defective component? (c) What proportion of the finished subassemblies will contain at least one defective component? (d) What proportion of the finished subassemblies will contain more than one defective component? (e) What proportion of the finish?

Explanation / Answer

as subssembly is made up of 3 components a,b,c and all three are having defective percentage then the components combined defective percentage will be = 5%+10%+4% = 19%

therefore the probability of defective = 0.19

probability of non defective = 0.81

n = 3

a) p(x=0) = 3C0*(0.19)^0*(0.81)^3 = 0.531 = 53.1%

B) P(X=1) = 3C1*(0.19)^1*(0.81)^2 = 0.186 = 18.6%

C) P(X>=1) = 1 - P(X=0)

P(X=0) = 0.186(AS CALCULATED IN B)

THERE P(X>=1) = 1 - 0.0.531 = 0.469

D) P(X>1) = 1-P(X=0)-P(X=1)

= 1 - 0.186 -0.531 = 0.283

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