Question

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

Short answer

The probability that$x$falls in the shaded area is$0.625$

Step-by-step solution

Given Information 

Given in the question is a graph,

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

Calculation

The following value is indicated based on the information provided in the question:

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{8},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\le x\le 8.5\\ 0,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{otherwise}\end{array}\right.$

Let's consider the graph first,

The shaded region is $0\le x\le 5$

Therefore, the probability of the shaded region will be,

$P(0\le x\le 5)={\int }_0^5 \frac{1}{8}dx$

$=\frac{1}{8}[x{]}_0^5$

$=\frac{1}{8}[5-0]$

$=\frac{5}{8}$

$=0.625$