Chapter 11.8, Problem 25E

To determine

TO-DETERMINE the complement of the probability.

Answer to Problem 25E

The probability that neither the student nor his/her friend will be chosen to give the first speech is $\text{P}\left(\text{not A}\right)=\frac{5}{6}$ .

Explanation of Solution

Given information:

Consider, the total students in the class is $12$ .

Calculation:

The probability of one student and his/her friend to be chosen to give the speech is $\text{P}\left(\text{A}\right)=\frac{2}{12}$ .

The probability that neither one particular student and his/her friend will be chosen to give the speech can be calculated by

  $\begin{array}{l}\text{P}\left(\text{not A}\right)=1-\text{P}\left(\text{A}\right)\left[\text{probability of complementary elements}\right]\\ \text{P}\left(\text{not A}\right)=1-\frac{2}{12}\left[\text{substitute }\frac{2}{12}\text{ for P}\left(\text{A}\right)\right]\\ \text{P}\left(\text{not A}\right)=\frac{10}{12}\left[\text{subtract}\right]\\ \text{P}\left(\text{not A}\right)=\frac{5}{6}\end{array}$

Hence, the probability that neither the student nor his/her friend will be chosen to give the first speech is $\text{P}\left(\text{not A}\right)=\frac{5}{6}$ .