Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. 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 fair because both hank and rosa will get a point if the letter y is drawn. 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 greater than the probability of rosa 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.

Explanation:

Step1: Count vowels and consonants

In the phrase "probability game", without considering 'y' for now, there are 5 vowels (a, o, a, i, a) and 9 consonants (p, r, b, b, l, t, y, g, m). When 'y' can be either, we still need to calculate probabilities. The total number of tiles is 15.

Step2: Calculate Hank's probability

The number of vowels considering 'y' as a vowel is 6. The probability of Hank drawing a vowel $P(Hank)=\frac{6}{15}=\frac{2}{5}$.

Step3: Calculate Rosa's probability

The number of consonants considering 'y' as a consonant is 9. The probability of Rosa drawing a consonant $P(Rosa)=\frac{9}{15}=\frac{3}{5}$.

Step4: Compare probabilities

Since $\frac{2}{5}<\frac{3}{5}$, the probability of Hank drawing a winning - letter is less than the probability of Rosa drawing a winning - letter.

Answer:

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.