Question

Hal and Renee play the following game: A bag has 14
tiles in it, each with a letter from the phrase the probability on it. Hal and Renee take turns drawing a tile, recording the letter, and placing the tile back in the bag. Renee earns a point if she draws a vowel. Hal earns a point if he 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 fair because both Hal and Renee will get a point if the letter y is drawn.


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


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


The game is not fair because the probability of Hal drawing a winning letter is more than the probability of Renee drawing a winning letter.

Answer 1

Answer: The fourth statement.

Reason: The 14 letters in "the probability" are t,h,e,p,r,o,b,a,b,i,l,i,t,y. If y is counted as a vowel, vowels = {e,o,a,i,i,y} = 6 and consonants = 8. If y is counted as a consonant, vowels = {e,o,a,i,i} = 5 and consonants = 9. In either case Hal’s probability (consonant) is larger than Renee’s (vowel), so the game is not fair because Hal has the higher chance of scoring.