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

To find the probability that a five-digit number has at least one zero in it, we can use the complementary probability approach. Let's go through the solution step-by-step:

1. First, calculate the total number of five-digit numbers. A five-digit number ranges from 10000 to 99999. Therefore, the total number of five-digit numbers is 99999 - 10000 + 1 = 90000.

2. Next, determine the number of five-digit numbers that do not contain any zeros. For a number to have no zeros:

   • The first digit (ten-thousands place) can be any digit from 1 to 9 (9 options), because it cannot be zero (as the number must be a five-digit number).
   • Each of the remaining four digits (thousands, hundreds, tens, and units places) can also be any digit from 1 to 9 (9 options each).

   Therefore, the total number of five-digit numbers with no zeros is 9^5. Calculating this gives:

   9^5 = 9 \times 9 \times 9 \times 9 \times 9 = 59049

3. Now, use the complementary probability to find the number of five-digit numbers with at least one zero:

   90000 - 59049 = 30951

4. Finally, calculate the probability that a five-digit number has at least one zero:

   Probability = \frac{30951}{90000}

   Simplifying the fraction gives approximately 0.344.

Therefore, the probability that a five-digit number has at least one zero in it is 0.344.