Answer to Question #160971 in Statistics and Probability for erma

Question

Five computers will be delivered to a certain school for testing, but three of them are defective. The principal will get two of these computers for his office. Let T represent the random variable representing the defective computers will occur. Find the values of random variable T.  

Answer 1

Given that out of $5$ computers 3 computers are defective.

The principal will get $2$ of those.

Out of $5$ computers $2$ can be choose in $^5C_2$ ways.

Therefore sample space $S$ contains $^5C_2$ number of points.

Out of $5$ computers principal will get $2$ computers in such way

(i) $2$ computers are defective and it can be choose in $^3C_2$ ways.

(ii) $1$ computer is defective and $1$ computer is good, it can be choose in $^2C_1×^3C_1$ ways.

(iii) $2$ computers are good and it can be choose in $^2C_2$ ways.

Let $T$ be a random variable representing number of defective computers.

Then $T$ can take the values $0,1,2.$

Now we will find the probabilities of each points corresponding to the random variable $T.$

$\therefore P(T=0)=$ probability of getting no defective computers

$=\frac{^2C_2}{^5C_2}=\frac{1}{10}$

$P(T=1)=$ probability of getting $1$ defective computer

$=\frac{^2C_1×^3C_1}{^5C_2}=\frac{6}{10}=\frac{3}{5}$

$P(T=2)=$ probability of getting $2$ defective computers

$=\frac{^3C_2}{^5C_2}=\frac{3}{10}$

Which are the required values of random variable $T.$