### Q: What is the probability of randomly guessing the last four digits of a telephone number correctly?

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### A: 1/10,000

Explanation: Each digit is chosen from the integers 0 through 9, which is ten possible choices for each digit. There are four digits to choose independently, so there are:

10 x 10 x 10 x 10 = 10,000 ways to choose the four digits.

Then, the one correct sequence of 4 digits, is one out of 10,000. The probability is 1/10,000.

Another way to arrive at the number 10,000 is as follows:

The 4-digit sequence may be anything from 0000 to 9999. So, how many is that? 9999 – 0000 +1 = 10,000. Why the ‘plus one’ on the end? If you just subtract the numbers, it tells you how many spaces there are between the numbers. Add one to include either the first number or the last number, whichever one has not been already counted.