Question

In Exercises 5–36, express all probabilities as fractions.

ZIP Code If you randomly select five digits, each between 0 and 9, with repetition allowed, what is the probability you will get the author’s ZIP code?

Short answer

The probability of getting the author’s ZIP code is equal to$\frac{1}{100000}$.

Step-by-step solution

Given information

Five digits are to be chosen from 0 to 9 to make the author’s ZIP code.

Define counting rule

The total number of possible ways of an event is theproduct of the number of possibilities at each step of the event.

The number of possibilities at each step can be counted.

Calculation

Let A be the event of getting the author’s ZIP code.

The number of digits from 0 to 9 is equal to 10.

The total number of ways in which five numbers can be chosen from 0 to 9 with repetition:

$10\times 10\times 10\times 10\times 10=100000$

The number of ways in which the author’s ZIP code can be formed is one.

The probability of getting the author’s ZIP code:

$$\begin{gathered} P\left(A\right)=\frac{\text{Number}\text{of}\text{favourable}\text{ways}}{\text{Total}\text{number}\text{of}\text{ways}} \\ =\frac{1}{100000} \end{gathered}$$

Therefore, the probability of getting the author’s ZIP code is equal to $\frac{1}{100000}$.