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 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 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 fair because hal and renee have the same probability of drawing a winning letter.

Explanation:

Step1: Count vowels and consonants

The word "probability" has 11 letters. Vowels (a, e, i, o, u) in "probability" are: o, a, i, i. If we consider y as a vowel, vowels count is \(4 + 1=5\). Consonants count is \(11 - 5 = 6\). Probability of Hal (vowel) \(P(H)=\frac{5}{11}\), probability of Renee (consonant) \(P(R)=\frac{6}{11}\).

Step2: Compare probabilities

Since \(\frac{5}{11}<\frac{6}{11}\), the probability of Hal drawing a winning letter is less than the probability of Renee drawing a winning letter.

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.