Question

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 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 greater than the probability of renee drawing a winning letter.

Explanation:

Step1: Count vowels and consonants

The word "probability" has 11 letters. Vowels are 'o', 'a', 'i', 'i', 'y' (5 vowels). Consonants are 'p', 'r', 'b', 'b', 'l', 't' (6 consonants).

Step2: Calculate probabilities

Probability of Hal (vowel) is $\frac{5}{11}$. Probability of Renee (consonant) is $\frac{6}{11}$. Since $\frac{5}{11}<\frac{6}{11}$.

Answer:

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.