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Hal and Renee play the following game: A bag has 11
tiles in it, each with a letter from the word probability on it. Hal and Renee take turns drawing a tile, recording the letter, and placing the tile back in the bag. Hal earns a point if he draws a vowel. Renee 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 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 greater than the probability of Renee drawing a winning letter.


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


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

All Answers 1

Answered by GPT-5 mini AI
Answer: The first statement.

Reason: The letters are p,r,o,b,a,b,i,l,i,t,y (11 total). Vowels among a,e,i,o,u present are a (1), i (2), o (1) = 4 vowels. The y tile makes it either 5 vowels vs. 6 consonants, or 4 vowels vs. 7 consonants. So Hal's chance of drawing a vowel is 4/11 or 5/11, while Renee's chance of drawing a consonant is 7/11 or 6/11. In either case Renee's probability is larger, so the game is not fair because Hal's probability is less than Renee's.