Three different machines M1, M2, and M3 are used to produce similar electronic c

Question

Three different machines M1, M2, and M3 are used to produce similar electronic components. Machines M1, M2, and M3 produce 20%, 30%, and 50% of the components respectively. It is known that the probabilities that the machines produce defective components are 1% for M1, 2% for M2. and 3% for M3. If a component is selected randomly from a large batch, and that component is defective., (a) Find the probability that it was produced by M3. (b) Find the probability that it was produced by M2. Round all your answers in 4 decimal places

Explanation / Answer

Pr(M1 produce) = 0.20 ; Pr(M2 Produce) = 0.30 ; Pr( M3 produce) = 0.50

Pr(Defective l M1) = 0.01 ; Pr(Defective l M2) = 0.02 ; Pr(Defective l M3) = 0.03

(a) Here component is selected randomly from a large batch and component is defective

Pr(Defective) = 0.01 * 0.20 + 0.02 * 0.30 + 0.03 * 0.50 = 0.023

Pr(Produced by M3 l Defective) = (0.03 * 0.50)/0.023 = 0.6522

(b) Pr(Prodcued by M2 l defective) = (0.02 * 0.30)/ 0.023 = 0.2609

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