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The lottery balls with the numbers 1, 2, 3, 4, 5, and 6 written on them...

The lottery balls with the numbers 1, 2, 3, 4, 5, and 6 written on them are placed in a container and well mixed, so that when drawing a ball, each ball in the container is equally likely. What is the probability that two balls with the same parity are drawn, if: (a) Two balls are drawn from the six balls without replacement? (b) Two balls are drawn from the six balls with replacement? For each part, express the set of sample points of the experiment in set-builder notation (preferred), or write them all out explicitly.

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