# Question # 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.

Probability
ANSWERED 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. 2021-02-22
We will first find the probability that we call a number which does not have zeros.
We have $$\displaystyle{10}^{{4}}={10000}$$
numbers to choose from (on each of the 4 places we can put any of the 10 digits). Also, we have $$\displaystyle{9}^{{4}}={6561}$$
numbers which do not have a zero (because on each of the 4 places we can put any of the 9 digits - we must exclude 0).
So, the probability is
$$\displaystyle\frac{{6561}}{{10000}}={0.6561}$$