Question

Find the probability that x falls in the shaded area.

Short answer

The probability that $x$falls in the shaded area is:$P(2.5\le x\le 5.5)=0.3$

Step-by-step solution

Given Information 

Given in the question that a graph.

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

Calculation

From the information, we know that

$f\left(x\right)=\left\{\begin{array}{l}\frac{1}{10},\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\le x\le 10\\ 0,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{otherwise}\end{array}\right.$

Let's consider the graph first, Where we obtain that the shaded region is $2.5\le x\le 5.5$.

Therefore, the probability of the shaded region will be,

$P(2.5\le x\le 5.5)={\int }_{2.5}^{5.5} \frac{1}{10}dx$

$=\frac{1}{10}[x{]}_{2.5}^{5.5}$

$=\frac{1}{10}[5.5-2.5]$

$=\frac{3}{10}$

$=0.3$