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

Expert verified

The probability of getting the author’s ZIP code is equal to1100000.

Step by step solution

01

Given information

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

02

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.

03

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:

10×10×10×10×10=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:

PA=NumberoffavourablewaysTotalnumberofways=1100000

Therefore, the probability of getting the author’s ZIP code is equal to 1100000.

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