Question

A shipment of 7 television sets contains 2 defective sets A hotel makes a random purchase of 3 of the sets: a) If x is the number of defective sets purchased by the hotel, find the probability distribution of x Express the results graphically as a probability histogram. b) Find the cumulative distribution function of the random variable X representing the number of defectives. Then using flx), find (a) p(X = 1); (b) p(O < X s 2).

Answer 1

N=7

m=2

n=3

Let X be number of defective sets bought by the hotel

$P(x,N,n,m)=\frac{\begin{pmatrix} M \\ x \end{pmatrix}\begin{pmatrix} N-m \\ n-x \end{pmatrix}}{\begin{pmatrix} N \\ n \end{pmatrix}}$

$P(x,N,n,m)=\frac{\begin{pmatrix} 2 \\ 0 \end{pmatrix}\begin{pmatrix} 7-2 \\ 3-0 \end{pmatrix}}{\begin{pmatrix} 7 \\ 3 \end{pmatrix}}$

$=\frac{\begin{pmatrix} 2 \\ 0 \end{pmatrix}\begin{pmatrix} 5 \\ 3 \end{pmatrix}}{\begin{pmatrix} 7 \\ 3 \end{pmatrix}}$

$=\frac{(1)(10)}{(35)}$

=0.2857