When four digits (between 0 and 9 inclusive) are randomly selected with replacement for a lottery ticket, what is the probability that at least one digit will be a zero?

We are asked to determine the probability of having at least one digit of zero in a winning lottery number that is composed of four digits from the set of numbers from 0 to 9. To determine the probability to be known, we can approach this problem by computing for the probability by counting theory for each digit.

Digit 1: there are 10 choices, so the probability is 1/10

Digit 2: there are only9 choices, probability of 1/9

Digit 3: there are also 9 choices, probability of 1/9

Digit 4: 9 digits as 0 is not a included

* (numbers beginning with zero do not count zero as part of the number)

Hence the probability is (1/10) * (1/9) * (1/9) * (1/9) = 0.000137