Question 167
Eva, Per and Anna play with their pocket calculators. They choose different integers and check, whether or not they are divisible by $11$. They only look at nine-digit numbers consisting of all the digits $1,2, \ldots, 9$. Anna claims that the probability of such a number to be a multiple of $11$ is exactly $1 / 11$. Eva has a different opinion: she thinks the probability is less than $1 / 11$. Per thinks the probability is more than $1 / 11$. Who is correct?