help with math problem

[furyshade]

this was given as extra credit, but no one in any of the classes this teacher has (highschool) got it that i know of, so wondering if we were missing something very obvious.

You have two hats, hat #1 has 8 red marbles and 2 blue marbles, hat #2 has 2 red marbles and 8 blue. you randomly select a hat and randomly choose two marbles from it, both of which are blue. you then switch hats and randomly pick out a marble, what is the probability that this will be a red marble?

usually we are not allowed calculators on these extra credit problems but for this one it said a calculator was allowed and to round to the third decimal place.