Question

When 4 digits between 0 and 9 are randomly selected with replacement for a lottery ticket, what is the probability that at least one digit is 7.

Answer 1

We will have the following:

We will be able to take 4 values, so:

*When we pick value 1: There will be 10 possible choices [1/ 10]

*When we pick value 2: There will be 9 possible choices [1/9]

*When we pick value 3: There will be 8 possible choices [1/8]

*When we pick value 4: There will be 7 possible choices [1/7]

So, the probability of that number being seven is the following:

$p=(\frac{1}{10})(\frac{1}{9})(\frac{1}{8})(\frac{1}{7})\Rightarrow p=\frac{1}{5040}\Rightarrow p=1.984126984\cdot10^{-4}$

So, the probability of at least one digit is 7 is 0.0001984126984.