Chapter 8.6, Problem 51E

To determine

To find: the probability of the event.

Answer to Problem 51E

The probability of selected all three numbers even is $\frac{1}{8}$ .

Explanation of Solution

Given information:

A random number generator selects three numbers from 1 through 10.

All three numbers are even

Calculation:

Consider the 1 to 10 numbers. Three numbers randomly selected from 1 to 10 numbers.

There are total 5 even numbers from 1 to 10, so probability of selecting one even number is,

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{5}{10}\\ =\frac{1}{2}\end{array}$

Since, the selection of all three numbers is independent events.

So, the probability that the selected three numbers even is product of individual probability of selecting one even number,

  $\begin{array}{c}P\left(E\right)=\frac{5}{10}\cdot \frac{5}{10}\cdot \frac{5}{10}\\ =\frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}\\ =\frac{1}{8}\end{array}$

Hence, the probability of selected all three numbers even is $\frac{1}{8}$ .