Equally Likely (Fair) Choice

Mentor: When we use a die for a game, we want the die to be fair. What does that mean?

Student: It means that your chances of getting each number on the die are the same. No one number is more likely to be chosen than any other number.

Mentor: Exactly. Each number is equally likely to be chosen. Suppose two players use a six-sided die that has the sides numbered 1,1,2,2,3 and 4. There are four numbers that can come up (1, 2, 3, and 4). Is the game fair if the first player wins when 1 or 2 shows, and the second player wins if 3 or 4 shows?

Student: No way! The first player will almost always win.

Mentor:Even though each player has two winning numbers, these numbers are not equally likely! Can you come up with more examples of games where numbers are or aren't equally likely to be chosen?

Students and mentor come up with examples.