Question

A shipment of five computer contains two that are slightly defective. If a retailer receive three of 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 of X of the random variable X representing the numbers computers purchased by 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)}.

Number of all possible samples: $C_5^3=10.$

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

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

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

$P(X=3)=0.$