Question

5) A bin contains 62 bolts, 28 have metric thread while the remainder have English thread. Suppose that 3 washers are selected without replacement from the lot. A) What is the probability that all 3 bolts have metric thread? B) What is the probability that the third bolt selected has English thread if the first and second bolts selected have metric threads? C) What is the probability that the second bolt selected has English thread if the first and

Answer 1

a)P(all three have metric thread)=(28/62)*(27/61)*(26/60)=0.0866

b)P(third has English thread given first 2 have metric thread)=34/60=0.5667 (as there remains 34 English thread among 60 thread if first 2 are metric thread)

c)

P(first and third are having metric threads)=P(first metric ; second English and third metric thread)+P(first metric ; second metric and third metric thread)

=(28/62)*(34/61)*(27/60)+(28/62)*(27/61)*(26/60)=0.1999

hence P(second is English given first and third are metric)

=P(first metric ; second English and third metric thread)/P(first and third are having metric)

=(28/62)*(34/61)*(27/60)/0.1999=0.5667