Answer to Question #288495 in Statistics and Probability for erica

Question

A shipment of 20 similar laptop computers to a retail outlet contains 3 that are defective. If a school makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives. Show the table in your solution. Round off answers to 4 decimal places.

Answer 1

Let $X=$ the number of defective computers purchased: $X=0,1,2.$

$$P(X=0)=\dfrac{\dbinom{3}{0}\dbinom{20-3}{2-0}}{\dbinom{20}{2}}$$

$$=\dfrac{1(136)}{190}=\dfrac{68}{95}$$

$$P(X=1)=\dfrac{\dbinom{3}{1}\dbinom{20-3}{2-1}}{\dbinom{20}{2}}$$

$$=\dfrac{3(17)}{190}=\dfrac{51}{190}$$

$$P(X=2)=\dfrac{\dbinom{3}{2}\dbinom{20-3}{2-2}}{\dbinom{20}{2}}$$

$$=\dfrac{3(1)}{190}=\dfrac{3}{190}$$

The probability distribution for the number of defectives

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 0 & 1 & 2 \\ \hline p(x) & 0.7158 & 0.2684 & 0.0158 \\ \end{array}$$