Imagine a Game Show on Television Where One Lucky Contestant

Imagine a game show on television where one lucky contestant is presented with four upside-down buckets that are numbered 1, 2, 3, and 4. Under one of the buckets is a $100 bill. Under each of the other three buckets is a $10 bill. After the game ends, the contestant will receive the amount of money that is under his or her bucket.
The host of the game show asks the contestant to choose one of the four buckets. After the contestant makes a choice, the host lifts one of the remaining three buckets to reveal a $10 bill under it. At this point, three buckets remain uncovered: the bucket that the contestant originally chose and the two buckets that were not uncovered by the host.
The host subsequently asks the contestant if he or she would like to keep the original bucket or change buckets to one of the two other buckets remaining.

-Nancy tosses a fair coin five times and gets heads each time. When her son Shane asks her about the probability of getting tails on the next (sixth) toss, Nancy says the following: "This is a fair coin, so I should toss heads approximately 50% of the time. Because I have tossed heads 100% of the time for my first five tosses, then the probability of me tossing tails on the sixth toss must be greater than 50%." Nancy's statement is an example of the:

A) hot-hand fallacy.
B) association fallacy.
C) gambler's fallacy.
D) dealer's fallacy.
E) Showtime fallacy.