Chapter 12.1, Problem 68S

To determine

Find the probability that the girls are separated.

Answer to Problem 68S

The chances that the girls separated is $66.7\%$ .

Explanation of Solution

Given:

It is given in the question that two boys and two girls are lined up at random and also a girls is on an end.

Concept Used:

In this, use the concept of probability and some concept of percentage.

Calculation:

Here, Probability of a girl on the end, the other girl next to her, the two boys on the other end.

  $\frac{2}{4}\times \frac{2}{3}\times \frac{1}{2}\times \frac{1}{1}\times 2=\frac{8}{24}=\frac{1}{3}$ and $\frac{1}{3}$ can be written like $33.3\%$ chance that the girls will be together.

So, the chance that all will be separated is $100\%-33.3\%=66.7\%$ .

Conclusion:

The chances that the girls separated is $66.7\%$ .