Question

A machine manufacturing screws is known to produce 5% defectives. In a random sample of 15 screws the probability that there are exactly 3 defectives is

• A. ${\left(\frac{1}{2}\right)}^3$
• B. ${\left(\frac{19}{20}\right)}^3$
• C. ${}^{15}{C}_3{\left(\frac{19}{20}\right)}^{12}{\left(\frac{1}{20}\right)}^3$
• D. ${\left(\frac{1}{20}\right)}^3$

Answer 1

Answer: (C)

${}^{15}{C}_3{\left(\frac{19}{20}\right)}^{12}{\left(\frac{1}{20}\right)}^3$

A machine manufactures 5% defective screws. Probability of defective screws = $\frac{5}{100}=\frac{1}{20}$
In sample of 15 screws; $n=15$
Probability that there are exactly 3 defectives = ${}^n{C}_k{p}^k{(1-p)}^{n-k}$
= ${}^{15}{C}_3{\left(\frac{1}{20}\right)}^3{(1-\frac{1}{20})}^{15-3}$

= ${}^{15}{C}_3{\left(\frac{1}{20}\right)}^3{\left(\frac{19}{20}\right)}^{12}$