Chapter 13.2, Problem 1CYU

To determine

To Find: The probability that the shapes are arranged in the correct order.

Answer to Problem 1CYU

The probability that the polygons are in correct order is $\frac{2}{5}$ .

Explanation of Solution

Given:

The give diagram is shown in Figure 1

  

Figure 1

Calculation:

Since, the number of polygons are 5 with sides 3, 4, 5, 6, 8 then the number of simple events in the sample space is $n\left(S\right)=C\left(5,2\right)$ .

Consider the event E is the event for obtaining two polynomial in order of the sides then the possible cases to the event is E is,

  $\left(3,4\right),\left(4,5\right),\left(5,6\right),\left(6,8\right)$

Hence, the value of $n\left(E\right)=4$ .

Thus, the probability for the event is,

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{4}{C\left(5,2\right)}\\ =\frac{4}{10}\\ =\frac{2}{5}\end{array}$

Thus, the proababiltiy that the polygons are in correct order is $\frac{2}{5}$ .