Chapter 13.4, Problem 31SPR

To determine

To calculate:

Probability of the given event.

Answer to Problem 31SPR

Probability of the given event $P\left(Xison\overline{RT}\right)$ is $0.57$ .

Explanation of Solution

Given information:

Event: $P\left(Xison\overline{RT}\right)$

It is given that point $X$ is chosen at random on $\overline{QT}$ .

The line segment $\overline{QT}$ is described by the following line that contains points $Q,R,S,T$ .

  

For finding the probability that a point, $X$ is on $\overline{QS}$ divide the length of $\overline{QS}$ by length of $\overline{QT}$ .

  $P\left(Xison\overline{RT}\right)=\frac{L_{\overline{RT}}}{L_{\overline{QT}}}$

Where,

  $L_{\overline{RT}}=$ length of $\overline{RT}$

  $L_{\overline{QT}}=$ Length of $\overline{QT}$

  $\begin{array}{l}P\left(Xison\overline{RT}\right)=\frac{3+5}{6+3+5}\\ =\frac{8}{14}\\ =0.57\end{array}$

Therefore, Probability of the given event is $0.57$ .