Chapter 11.9, Problem 25E

To determine

To find the probability that the last two digits of a randomly generated $5$ -digit number are both $4$ .

Answer to Problem 25E

  $\frac{1}{100}$

Explanation of Solution

Given information:

A digit can be used more than once. A $5$ -digit number is randomly generated.

The given options are:

  $\frac{1}{100}$

  $\frac{1}{90}$

  $\frac{1}{81}$

  $\frac{1}{10}$

Calculation :

Each digits can be used more than once, so it is an independent event.

As there are ten digits, the probability of randomly choosing the number $4$ is $\text{P}\left(4\right)=\frac{1}{10}$

The probability of randomly choosing another $4$ is:

  $\text{P}\left(\text{4 and 4}\right)=\frac{1}{10}\times \frac{1}{10}=\frac{1}{100}$

Hence, the probability of randomly generating a $5$ -digit number with the last two digits both being $4$ is $\frac{1}{100}$ .