Answer to Question #297972 in Statistics and Probability for Mae

Question

A shipment of five computers contains two that are slightly defective. if a retailer receives three of these computers at random, list the elements of the sample paces using the letters D and N for defective and non-defective computers,respectively. To each sample point assign a value x of the random variable X representing the number of computers purchased by the ratailer which are slightly defective.

Answer 1

Sample space:

$$S=\{NNN, NND,NDN,DNN, NDD,$$

$$DDN, DND\}$$

Let $X=$ the number of slightly defective computers. The possible values of $X$ are

$0,1,2.$

$$P(X=0)=\dfrac{\dbinom{2}{0}\dbinom{5-2}{3-0}}{\dbinom{5}{3}}=\dfrac{1(1)}{10}=\dfrac{1}{10}$$

$$P(X=1)=\dfrac{\dbinom{2}{1}\dbinom{5-2}{3-1}}{\dbinom{5}{3}}=\dfrac{2(3)}{10}=\dfrac{3}{5}$$

$$P(X=2)=\dfrac{\dbinom{2}{2}\dbinom{5-2}{3-2}}{\dbinom{5}{3}}=\dfrac{1(3)}{10}=\dfrac{3}{10}$$