The game is relatively fair as both Hank (who scores with vowels) and Rosa (who scores with consonants) have similar chances of earning points. The fairness can slightly tilt in favor of one player or the other based on how they decide to classify the letter 'y'.
To determine whether the game Hank and Rosa are playing is fair, we need to evaluate the probability of drawing a vowel versus a consonant, including the special case of the letter 'y', which can be considered both.
The phrase 'probability game' contains the following vowels: a, i, o, a, i, and e, totaling 6 vowels. It also contains the following consonants: p, r, b, l, t, g, m, which amount to 7 consonants. The letter 'y' appears once and can be considered either a vowel or a consonant based on their game rules.
Hank earns a point for drawing a vowel. Without considering 'y', the probability of Hank drawing a vowel is 6 out of 15. If 'y' is considered a vowel, this probability increases to 7 out of 15. For Rosa to earn a point, she must draw a consonant. Without considering 'y', the probability of Rosa drawing a consonant is 7 out of 15. If 'y' is considered a consonant, the probability is 8 out of 15.
By comparing these probabilities, we can see that neither player has a significant advantage, and the game can be considered relatively fair. However, if 'y' is more likely to be considered a vowel, Hank might have a slight advantage, and if it's more likely to be considered a consonant, Rosa might have an edge. Ultimately, the fairness of the game could depend on how they agree to treat the letter 'y'.
The probable question may be:
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?