Question

What is the probability that a five-digit number has at least one zero in it?

• A. 0.296
• B. 0.314
• C. 0.344
• D. 0.412
• E. 0.442

Answer 1

The Correct Option is C

The correct answer is option (C):

0.344

Let's break down how to solve this probability problem. We want to find the probability that a five-digit number contains at least one zero. It's often easier to calculate the probability of the *opposite* event (no zeros) and subtract it from 1.

First, let's consider the total number of five-digit numbers. The smallest five-digit number is 10,000, and the largest is 99,999. Therefore, there are 99,999 - 10,000 + 1 = 90,000 total five-digit numbers.

Now, let's determine the number of five-digit numbers that have NO zeros.

* The first digit can be any digit from 1 to 9 (9 choices).
* The second digit can be any digit from 1 to 9 (9 choices).
* The third digit can be any digit from 1 to 9 (9 choices).
* The fourth digit can be any digit from 1 to 9 (9 choices).
* The fifth digit can be any digit from 1 to 9 (9 choices).

So, the number of five-digit numbers with no zeros is 9 * 9 * 9 * 9 * 9 = 9^5 = 59,049.

The probability of a five-digit number having *no* zeros is the number of five-digit numbers with no zeros divided by the total number of five-digit numbers: 59,049 / 90,000 = 0.6561.

Now, to find the probability of having *at least one* zero, we subtract the probability of *no* zeros from 1: 1 - 0.6561 = 0.3439.

This is very close to 0.344. Rounding to three decimal places, the answer is 0.344. Therefore, the probability that a five-digit number has at least one zero in it is approximately 0.344.