Chapter 10.6, Problem 18E

To determine

To calculate:

The probability value of $x$ is greater than $2$

Answer to Problem 18E

The probability value of $x$ is greater than $2$ is $0.9$ .

$x$	$1$	$2$	$3$	$4$
$P\left(x\right)$	$0.1$	$0.3$	$0.4$	$0.9$

Explanation of Solution

Given Information:

$x$	$1$	$2$	$3$	$4$
$P\left(x\right)$	$0.1$	$0.3$	$0.4$

Probability distribution for the random variable: $x=4$

Calculation:

The sum of probability in probability distribution sums upto $1$ .

The required probability is as follows:

  $P\left(x=4\right)=1-\left[P\left(x=1\right)+P\left(x=2\right)+P\left(x=3\right)\right]\mathrm{...}\left(1\right)$

Put the values in equation (1)

  $\begin{array}{l}P\left(x=4\right)=1-\left(0.1+0.3+0.4\right)\\ P\left(x=4\right)=1-0.8\\ P\left(x=4\right)=0.2\end{array}$

The probability values of $x$ is greater that $2$ is:

  $P\left(x>2\right)=P\left(x=2\right)+P\left(x=3\right)+P\left(x=4\right)\mathrm{...}\left(2\right)$

Put the values in equation (2)

  $\begin{array}{l}P\left(x>2\right)=0.3+0.4+0.2\\ P\left(x>2\right)=0.9\end{array}$

The probability value of $x$ is greater than $2$ is $0.9$ .

$x$	$1$	$2$	$3$	$4$
$P\left(x\right)$	$0.1$	$0.3$	$0.4$	$0.9$