Chapter 6.7, Problem 21E

To determine

To find : the probability that the eventdoes not occur.

Answer to Problem 21E

The probability of not rolling a 1 is $\frac{5}{\text{6}}$ and the probability that the event does not occur is $\frac{n-1}{n}$ .

Explanation of Solution

Given information :

The probability of rolling 1 on a number cube is $\frac{1}{6}$ .

Calculation :

Here, the number of favourable outcome in not rolling a 1 is 5(2, 3, 4, 5 and 5) and total number of favourable outcome is 6.

Thus, the probability of not rolling a 1 is

  $\begin{array}{l}P\left(\text{Not rolling a 1}\right)=\frac{\text{Number of favourable outcomes}}{\text{Number of posssible outcome}}\\ P\left(\text{Not rolling a 1}\right)=\frac{5}{\text{6}}\\ P\left(\text{Not rolling a 1}\right)=\frac{5}{\text{6}}\end{array}$

In general if the probability of an event is $\frac{1}{n}$ , the probability that the event does not occur is

  $\begin{array}{l}P\left(\text{Does not occur}\right)=1-\frac{1}{n}\\ P\left(\text{Does not occur}\right)=\frac{n-1}{n}\end{array}$

Hence,

The probability of not rolling a 1 is $\frac{5}{\text{6}}$ and the probability that the event does not occur is $\frac{n-1}{n}$ .