Chapter 12.6, Problem 33E

To determine

To find:The probability of choosing enough information.

Answer to Problem 33E

The probability of choosing enough information is $\frac{7}{120}$ .

Explanation of Solution

Given information:

  

The combinations of three given statements provide enough information are,

  $\begin{array}{l}SSS\text{congruence}\text{}\text{theorem}\\ SAS\text{congruence}\text{theorem}\\ ASA\text{congruence}\text{theorem}\\ AAS\text{congruence}\text{theorem}\end{array}$

Now if we choose three statements from the given six, then population volume is given by $\begin{array}{c}\\ n=6\times 5\times 4\\ =120\end{array}$

Here,

Probability of $SSS$ is one

Probability of $SAS$ is three

Probability of $ASA$ is three

In these three, $AAS$ is a special case that leads to $ASA$ so the probability of $AAS$ is zero.

Now, the probability of choosing enough information is the ratio of the sum of three statements of six to the population volume.

Hence,

  $\begin{array}{c}\frac{SSS+SAS+ASA}{n}\\ =\frac{1+3+3}{120}\\ =\frac{7}{120}\end{array}$

Therefore, the probability of choosing enough information is $\frac{7}{120}$ .