Question

A bag contains 26 tiles showing a different letter from A to Z. Each player draws a letter tile at random. Player 1 wins if the letter is in his or her name. Player 2 wins if the letter is in his or her name. If the letter is in both their names then no one wins. Nathan and Katie play the game. Is this a fair game? If not, who has the advantage?

Answer 1

no

Explanation:

Nathan has 6 letters in his name so he has a higher chance of winning

Answer 2

No, Katie has the advantage.

Katie has 5 distinct letters.

Nathan has 4 distinct letters.

They have one overlap (a).

Katie can expect to win 4 out of 26 games.

Nathan can expect to win 3 out of 26 games.

Since Katie has more distinct letters, she has the advantage, so it is not a fair game.