The vaccine can be purified by one of three different machines:Machine A, Machin

Question

The vaccine can be purified by one of three different machines:Machine A, Machine B or Machine C.

• The probability of a defect if Machine A is used is 0.005.
• The probability of a defect if Machine B is used is 0.010.
• The probability of a defect if Machine C is used is 0.05.

Of 1200 products sampled, 420 were processed on Machine A, 510 wereprocessed on Machine B and the remainder on Machine C.

• Given that there is a defect, what is the probability that itwas processed on:

• Machine A?
  
• Machine B?  
  
• Machine C?

Explanation / Answer

P(defect)=(1/3)*0.005+(1/3)*0.01+(1/3)*0.05 = 0.0217 (1) Machine A: P(Machine A | defect)=P(Machine A and defect)/P(defect)                                =(1/3)*0.005/0.0217                                =0.0768 (2) Machine B: P(Machine B | defect)=P(Machine B and defect)/P(defect)                                =(1/3)*0.01/0.0217                                =0.1536 (3) Machine C: P(Machine C | defect)=P(Machine C and defect)/P(defect)                                =(1/3)*0.05/0.0217                                =0.768

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