SOLUTION: 5. (a) A production process comprises of two separate processes, moulding and assembly. It is known that the probability of a defect occurring in both processes is 0.03 and the pr

Question 328479: 5. (a) A production process comprises of two separate processes, moulding and assembly. It is known that the probability of a defect occurring in both processes is 0.03 and the probability of a defect occurring in the assembly process is 0.2.
(i) If it is assumed that the occurrence of a defect is independent of the process, calculate the probability of a defect occurring in either process.
(ii) Calculate the probability that an item will not contain a defect.
(iii) If a sample of three items are selected at random from the production output, what is the probability that at least one of them will have a defect?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
5. (a) A production process comprises of two separate processes, moulding and assembly.
It is known that the probability of a defect occurring in both processes is 0.03 and the probability of a defect occurring in the assembly process is 0.2
P(mould and assemb) = 0.03
P(assemb) = 0.2
Therefore P(mould) = 0.03/0.2 = 0.15
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(i) If it is assumed that the occurrence of a moulding defect is independent of the defect in the assemply process, calculate the probability of a defect occurring in either process.
P(mould OR assemb)= P(mould) + P(assemb) - P(mould AND assemb)
= 0.15+0.2 - 0.03 = 0.32
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(ii) Calculate the probability that an item will not contain a defect.
P(no defect) = 1-[P(m OR p)+P(m AND p)] = 1-[0.32+0.03] = 0.65
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(iii) If a sample of three items are selected at random from the production output, what is the probability that at least one of them will have a defect?
0.65^3 = 0.2746
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Cheers,
Stan H.
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