Question

Hank and Rosa play the following game: A bag has 15
tiles in it, each with a letter from the phrase probability game on it. Hank and Rosa take turns drawing a tile, recording the letter, and placing the tile back in the bag. Hank earns a point if he draws a vowel. Rosa earns a point if she draws a consonant. They decide that the letter y can be a vowel or a consonant. Which statement best explains whether or not the game is fair?


The game is not fair because the probability of Hank drawing a winning letter is greater than the probability of Rosa drawing a winning letter.


The game is fair because Hank and Rosa have the same probability of drawing a winning letter.


The game is not fair because the probability of Hank drawing a winning letter is less than the probability of Rosa drawing a winning letter.


The game is fair because both Hank and Rosa will get a point if the letter y is drawn.

Answer 1

Answer: The third statement.

Reason: The letters in "probability game" are p r o b a b i l i t y g a m e (15 total). Vowels (a, e, i, o, and possibly y) occur 6 times if y is a consonant (a(2)+e(1)+i(2)+o(1)), so Hank's probability = 6/15 while Rosa's = 9/15. If y is treated as a vowel, Hank's probability = 7/15 and Rosa's = 8/15. In either case Hank's probability is less than Rosa's, so the game is not fair.