Answer to Question #307004 in Statistics and Probability for Sheng

Question

There were 8 brand new laptops delivered to a retail outlet. Of the 8 laptops, 3 are defective. If a company makes a random purchase of 2 laptops, Find the probability distribution and the expected value for the number of defective laptops.

Answer 1

Let X be a random variable representing the number of the defective laptops, then X= {0, 1, 2}

$P(X=0)={\frac {{5 \choose 2}} {{8 \choose 2}}}={\frac {10} {28}}={\frac 5 {14}}$

$P(X=1)={\frac {{5 \choose 1}*{3 \choose 1}} {{8 \choose 2}}}={\frac {15} {28}}$

$P(X=2)={\frac {{3 \choose 2}} {{8 \choose 2}}}={\frac 3 {28}}$

$E(X)=0*{\frac 5 {14}}+1*{\frac {15} {28}}+2*{\frac 3 {28}}={\frac {21} {28}}={\frac 3 4}$