Flipping the coin twice gives you only one possibility of getting a 0 and 0.

Flipping the coin twice gives you two possibilities of getting a 0 and 1: (0 and 1) and (1 and 0)

Flipping the coin twice gives you only one possibility of getting a 1 and a 1.

So there are 4 possible results, thus the probability of getting two 0's is 1/4, the probability of getting a 0 and a 1 is 2/4, and the probability of getting two 1's is 1/4.

Now what are all the possible results for flipping the coin 4 times? etc.

-Dan