Question

topic: probability
progress
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
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 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.
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

In the word "probability", the vowels are 'o', 'a', 'i', 'i', 'y' (counting y as a vowel here), so there are 5 vowels. The consonants are 'p', 'r', 'b', 'b', 'l', 't', 'y' (counting y as a consonant here), so there are 6 consonants.

Step2: Calculate probabilities

The probability of Hal drawing a vowel, $P(Hal)=\frac{5}{11}$. The probability of Renee drawing a consonant, $P(Renee)=\frac{6}{11}$. 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.