Answer to Question #299287 in Statistics and Probability for Xzhely

Question

A shipments of five computers contains that are slightly defective. If a retailer receives three of these computers at random list the elements of the sample space 5 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 bu the retailer which are slightly defective

Answer 1

Elements of the sample space: {(N,N,N),(N,N,D),(N,D,N),(D,N,N),N,D,D).(D,N,D),(D,D,N)}.

$P(X=0)=\frac{C_2^0C_3^3}{C_5^3}=\frac{1}{10}.$

$P(X=1)=\frac{C_2^1C_3^2}{C_5^3}=\frac{3}{5}.$

$P(X=2)=\frac{C_2^2C_3^1}{C_5^3}=\frac{3}{10}.$

$P(X=3)=0.$