Question

If 10% of all disk drives produced on an assembly line are defective, what is the probability that there will be exactly one defect in a random sample of 5 of these? What is the probability that there will be no defects in a random sample of 5?

Answer 1

solution:

p=ncx ,. p^x.Q^{n-x}\\

where p and q are the probabilities of success and failure respectively.\\

in this case p =0.10 and Q=0.90\\

ncx= \frac{n!}{x!(n-x!)}\\

p(exactly one defect in a random sample of 5)\\

=5(0.10)^1(0.90)^4=0.3281\\

p(no. defects in a random sample of 5)\\

=1(0.90)^5=0.5905