At least how many times must you flip a fair coin before there is at least a 50% probability that you will get at least three heads?

Six times.

Step-by-step explanation:

Any time you flip a coin, there is a 50% probability of getting heads or tails. This means if you flipped it twice, you should get one head and one tail. Therefore, if you flipped it six times, you should get three heads and three tails.