A bucket has 2 marbles numbered 1 and 2. Randomly select one and put it back along with another marble with same number. Now select a second and put it back along with marble with sum of your first two picks (if you got the numbers 1 and 2 then there are now four marbles with the numbers: 1,1,2,3). Select a third marble.
a) Find P(sum of the three is odd).
b) Find P(first number was 2 | sum=odd).