Alphabet game word problem

Question

The alphabet game costs .25 to play. Before the game, 26 slips of paper, each with a different letter of the alphabet on it, are put into a bag. A player draws one slip from the bag. If the player draws a vowel (a, e, I, o, u) they win 1$

A. What is the probability of winning the game

B. What is the probability of losing a game

c. If a player plays 26 times how much money would you expect the player to win or lose. Explain your reasoning. 

Answer 1

We should assume that the slip of paper is returned to the bag after each game, so that each game begins with a full set of 26 letters. There being 26 letters, there is always 1/26 chance of drawing any particular letter in one draw.

A. There being 5 vowels, there is a 5/26 chance of drawing a vowel, thus winning the game.

B. There are 21 non-vowels (26-5), so there is a 21/26 chance of losing the game.

C. We expect in 26 draws to draw 5 vowels, but chance is fickle & we might draw more or fewer than 5. A player who plays 26 times pays $8.50 (26x0.25) & expects to win $5 (5x$1), a net loss of $3.50. This is why casinos stay in business!