Chapter 13.2, Problem 5CYP

To determine

To Find: The probability that all the points lie on the same straight line.

Answer to Problem 5CYP

The required probability is $0.0714$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider there are 8 points on the rectangle A, B, C, D, E, F, G, H.

Consider any three points without any restriction and the possible number of ways are,

  $\begin{array}{c}\left(\begin{array}{c}8\\ 3\end{array}\right)=\frac{\left(8\right)\left(7\right)\left(6\right)}{3!}\\ =56\end{array}$

Now consider the three points with the restriction that chosen three points are on the same line and then the number of ways to select the points are $\left(ABC\right),\left(CDE\right),\left(EFG\right),\left(GHA\right)$ .

Then, the P point lie on the same line segment and the probability is,

  $\begin{array}{c}P=\frac{4}{56}\\ =\frac{1}{14}\\ =0.0714\end{array}$

The required probability is $0.0714$ .