The probability of a part being produced having a materials defect (M) is 0.07,

Question

The probability of a part being produced having a materials defect (M) is 0.07, and the probability of a processing error (E) is 0.04. The probability of having both a defect and a processing error is 0.015.

A. Describe the set M U E in words, then find its probability.

B. What is the probability of producing a part with no defects or errors?

C. What is the probability of a processing error, given that there is a defect in the materials for the part?

D. Are the marterials defect and processing error events independent? Justify your answer.

Explanation / Answer

a)MUE reperesent probabitly of part being defetive or in a processing error or both

Probabilty =P(MUE)=P(M)+P(E)-P(M & E)=0.07+0.04-0.015=0.095

b) probability of producing a part with no defects or errors =1-P(MUE)=1-0.095=0.905

c) probability of a processing error, given that there is a defect in the materials for the part

=P(E|M)=P(M&E)/P(M)=0.015/0.07=0.2143

D)No as P(M)*P(E)=0.0028 which is not equal to P(M &E) =0.015 they are not independent

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