Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). find the probability that for one such phone number, the last four digits include at least one 0.

The complementary event of that the last four digits include at least one 0 is that the last four digits do not include any 0. So, for the first digit, there are 9 ways to pick a digit from 1 to 9. Similarly, there are 9 ways to pick each of other digits. Then the probability that a 4-digit numbers that do not include 0 is chosen is (9*9*9*9) / 10^4 = 0.6561. So the probability that the last four digits include at least one 0 is 1 - 0.6561 = 0.3439