Question

2-189. A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that 3 washers are selected at random, without replacement, from the lot. (a) What is the probability that all 3 washers are thicker than the target? (b) What is the probability that the third washer selected is thicker than the target if the first 2 washers selected are thinner than the target? (c) Wat is the probability that the third washer selected is thicker than the target?

Answer 1

a)P(all three are thicker then the target)=P(selecting all three from 30 thicker washers)

=³⁰C₃/⁵⁰C₃ =(30/50)*(29/49)*(28/48)=0.2071

b)

P(third is thicker given first 2 are thicker)=28/48=7/12=0.5833 (as there remains 28 thicker washer out of 48 remaining if first two are thicker)

c)P(third is thicker) =30/50 =3/5 =0.6 (as no prior information is available and there are 30 thicker washer out of total 50 washers)