### Instruction: A five-digit integer will be chosen at random from all possible positive five-digit integers. What is the probability that the number's units digit will be less than 5? Express your answer as a common fraction.### Response: I need to find the number of possible five-digit integers whose units digit is less than 5, and divide that by the total number of possible five-digit integers.
To find the total number of possible five-digit integers, I can use the fundamental counting principle.
There are 9 choices for the first digit, since it can't be 0.
There are 10 choices for each of the remaining four digits, since they can be any of the digits from 0 to 9.
So the total number of possible five-digit integers is 9 * 10 * 10 * 10 * 10 = 90,000.
To find the number of possible five-digit integers whose units digit is less than 5, I can use a similar approach.
There are still 9 choices for the first digit, and 10 choices for the second, third, and fourth digits.
But for the units digit, there are only 5 choices, since it can be 0, 1, 2, 3, or 4.
So the number of possible five-digit integers whose units digit is less than 5 is 9 * 10 * 10 * 10 * 5 = 45,000.
Therefore, the probability that a randomly chosen five-digit integer will have a units digit less than 5 is 45,000 / 90,000, which simplifies to 1/2.