Algerbra 2 Probablitiy Problem?

Question

Ive been trying forever and I cant get the answer. If anyone knows how to work this out, please feel free to help out. Also, Please explain how you did it so can understand how to do it. Thanks!

If Jack and Jill each flip a coin three times, what is the probability they will get the same number of heads?

Answer 1

Here are the possible outcomes from 3 flips:
TTT = 0 heads = 1/8
HTT, THT, TTH = 1 head = 3/8
HHT, HTH, THH = 2 heads = 3/8
HHH = 3 heads = 1/8

So the possible ways to get the same number of heads would be:
0 heads and 0 heads = (1/8)² = 1/64
1 head and 1 head = (3/8)² = 9/64
2 heads and 2 heads = (3/8)² = 9/64
3 heads and 3 heads = (1/8)² = 1/64

All together:
1/64 + 9/64 + 9/64 + 1/64 = 20/64 = 5/16