Question

Problem #1 (8 pts) Suppose a textbook with 4 the book. What is the probability that a particular page has 50 pages has 200 misprints which is distributed randomly throughout 3 or more misprints? Problem #2 (8 pts): A box contains 8 large, 5 medium, and 3 small bolts and another box contains 6 nuts which fits the large bolts, 4 nuts which fits the medium bolts and 2 nuts which fits the small bolts. If one bolt and one nut are picked at random from the two boxes, what is the probability that the nut fits the bolt?

Answer 1

P1) The error rate is   ${200\over 450}={4\over 9}$

Using Poisson distribution with $\lambda ={4\over 9}$ gives

Probability of r number of errors in a page is $P(r)=e^{-4/9}{(4/9)^r\over r!}~~~~~~~~~~~~r=0,1,2,....$

Required probability is

$1-[P(0)+P(1)+P(2)]=1-e^{-4/9}\left [ 1+{4\over 9}+{16\over 162} \right ] \\ ~~ ~~~~~~~~~~\hspace{3cm}~~~~\approx 0.0105$