Question

Find the probability that $x$falls in the shaded area.

Short answer

The probability that $x$falls in the shaded area is$0.22$

Step-by-step solution

Given Information 

Given in the question that a shaded graph,

We need to find the probability that$x$falls in the shaded area.

Solution 

According on the information provided, the following value is indicated:

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{9},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\le x\le 9\\ 0,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{otherwise}\end{array}\right.$

Let's consider the graph first, the shaded region is $6\le x\le 8$.

Therefore, the shaded region will be,

$P(6\le x\le 8)={\int }_6^8 \frac{1}{9}dx$

$=\frac{1}{9}[x{]}_6^8$

$=\frac{1}{9}[8-6]$

localid="1650465993463" $=\frac{2}{9}$

$=0.22$