Question

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Answer 1

Let p=Probability of a success and q-probability of a failure

p=$\frac{5}{100}$=$\frac{1}{20}$ and

q=1-p=1-$\frac{1}{20}$=$\frac{19}{20}$

n=10,r=0,1

P(not more than one defective items)=P(X=0)+P(X=1)

=C(10,0)$C(10,0)\bigg(\frac{19}{20}\bigg)^{10}+C(10,1)\bigg(\frac{19}{20}\bigg)^9\bigg(\frac{1}{20}\bigg)$

=$\bigg(\frac{19}{20}\bigg)^9\bigg(\frac{19}{20}+\frac{1}{20}\bigg)=\frac{29}{20}\bigg(\frac{19}{20}\bigg)^9$