Question

A sample of 100 items is taken at random from a batch known to contain 40% defectives. What is probability that the sample contains: (i) at least 44 defectives, (ii) exactly 44 defectives?

Answer 1

This is a binomial probability case.

P(X=x) =$\binom {n} {k} p^n q^{n-x}$

n=100,p=0.4$\implies$ q=0.6

i) at least 44 defectives

P(X$\geq$ 44) =$\displaystyle \sum_{x=44}^{100} \binom {100}{x} 0.4^x 0.6^{100-x}$

=0.2365

ii) exactly 44

P(x=44) =$\binom {100} {44} *0.4^{44}*0.6^{56}$

=0.0576