Question

What is the probability that a two digit number does not have the digit 1?

Answer 1

First, let us find the probability that the two digit number has the digit 1 in it.
There are a total of 90 two digit numbers from 10 to 99.
Out of these, the following numbers have a 1 in them: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81 and 91. That’s a total of 18 numbers which have the digit 1.
The probability is $\frac{18}{90}$ = $\frac{1}{5}$.
Hence, the probability of not having the digit 1 in a two digit number is 1 – $\frac{1}{5}$ = $\frac{4}{5}$.