A single bolt is selected at random from a lot of 10,000 bolts. Three different

Question

A single bolt is selected at random from a lot of 10,000 bolts. Three different kinds of defects: A, B, and C are known to occur in these particular bolts. Defect type A occurs 1% of the time, Type B defects occur 0.5% of the time, and type C occurs 0.75% of the time. In addition, it is estimated that 0.25% have both type A and B defects, 0.30% have both type A and C, 0.20% have type B and C, and 0.10% have all three defects 1. What is the probability that the sample bolt has at least one of the three types of defects? 2. What is the probability the sample bolt is defect free? 2. What is the probability that the sample bolt has defect type A or B or C? 4. What is the probability that the sample bolt has defects type A and B or defects type A and C? 5. Suppose you randomly select 3 bolts from the lot without replacement. What is the probability that all three bolts have defect type A? (make any assumption you need to make to work your answer.)

Explanation / Answer

1) probability of at least one type of defect =P(AUBUC) =P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC) +P(AnBNC) =0.01+0.005+0.0075-0.0025-0.003-0.002+0.001=0.016

2)probability =1-0.016=0.984

3)P(A or B or C) =P(AUBUC)-P(AnB)-P(AnC)-P(BnC) +2P(AnBnC) =0.016-0.0025-0.003-0.002+2*0.001

=0.0105

4)P( A and B U A and C) =P( AnB)+P(A n C)-P(AnBnC) =0.0025+0.003-0.001=0.0045

5)probability =(100/10000)*(99/9999)*(98/9998)=0.00000097

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