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9 puzzles
How long until a six?
Roll a fair die until the first six.
One green ball changes the odds
A bag contains 10 balls. Its number of green balls K is chosen uniformly from 0 through 10; the rest are red. You draw a ball uniformly, see green, and set it aside.
A boy born on Tuesday
Choose a family uniformly from all two-child families, then keep only families with at least one boy born on a Tuesday.
Put the champion in the middle?
You must win two consecutive matches out of three. Your opponents are your teacher and a tennis champion. You can play teacher–champion–teacher, or champion–teacher–champion.
Heads, then tails
Flip a fair coin until heads–tails appears in consecutive flips.
The higher of two dice
Roll two fair six-sided dice. Your score is the larger number.
The coin with two heads
Choose uniformly among a fair coin, a two-headed coin, and a two-tailed coin. Flip it once and observe heads.
At least one boy
A two-child family is selected uniformly, then filtered to keep only families with at least one boy.
The door you did not choose
Three doors hide one prize. You choose a door. A host who knows the prize location opens another door with no prize, then offers you the remaining closed door.