What is the probability that a randomly selected three-digit number is divisible by 11?

We need to figure out the denominator first of the probability fraction

100-999

That is 900 digits

Ok so our denominator is 900

Now we need to figure out the numerator. We do this by finding all the three digit numbers divisible by 11

We try listing (I couldn't find any better way to do this

110

121

132

143

154

165

176

187

198

----

209

220

231

242

253

264

275

286

297

----

Notice how the first number's last two digits start from 10 then decreases to 9 at 200

notice how the last number last two digits start from 98 and decrease to 97 at 200

This means each hundred we have 9 numbers divisible by 11

This means that there are 9*9 (9 different hundreds) = 81 numbers 

We have the numerator which is 81 and the denominator which is 900

Simplifying we have \(\boxed{\frac{9}{100}}\)

Thanks CalculatorUser.

You have given the best answer 

BUT just as a little diversion, here is a little number fact for determining if a number is divisable by 11