Appropriate Level: Pre-Calc and beyond
The Card Trick:
Ask for a volunteer, who will then pick a card from a standard 52 card deck, show it to the class, and return it to the deck in the location of his/her choice. Shuffle the deck several times and offer the volunteer the opportunity to shuffle if he/she desires. Then randomly choose a card and pronounce with complete confidence, “here is your card.”
Case 1: You guess right and gain the reputation for being a master magician.
Case 2: You guess wrong and get to pose a very nice question. Tell the students: “Someday this is going to work. And it is going to be fantastic!” Then ask: “How many times would I need to perform this trick to have at least a 50% chance of being successfully at least once?”
1) How many regular 6-sided dice should you roll to have at least a 99% chance of getting at least one 5?
2) How many people must you meet to have a greater than 50% chance that at least one of them shares your birthday?