Question

a bag contains 8 pieces of paper, each with one of these letters written on it: a, b, c, e, k, l, m, and r. one piece of paper is drawn. match the outcome with the word that expresses its likelihood. likely the letter drawn is a vowel equally likely the letter drawn is one of the first ten letters in the alphabet. unlikely the paper drawn has one letter on it. impossible the letter drawn is a consonant certain the letter drawn is a p.

Explanation:

Step1: Identify vowels in the set

The set is {A, B, C, E, K, L, M, R}. Vowels are A, E. So 2 out of 8 are vowels. Probability = $\frac{2}{8}=\frac{1}{4}$, which is less than 0.5, so it's unlikely.

Step2: Identify letters among first - ten in the set

The first - ten letters are {A, B, C, D, E, F, G, H, I, J}. In the set {A, B, C, E, K, L, M, R}, 4 out of 8 are among the first - ten. Probability = $\frac{4}{8} = 0.5$, so it's equally likely.

Step3: Analyze the single - letter condition

All the papers have one letter on them. Probability = 1, so it's certain.

Step4: Identify consonants in the set

Consonants in the set {A, B, C, E, K, L, M, R} are B, C, K, L, M, R. So 6 out of 8 are consonants. Probability = $\frac{6}{8}=\frac{3}{4}$, which is greater than 0.5, so it's likely.

Step5: Analyze the presence of 'P'

There is no 'P' in the set {A, B, C, E, K, L, M, R}. Probability = 0, so it's impossible.

Answer:

Likely: The letter drawn is a consonant
Equally likely: The letter drawn is one of the first ten letters in the alphabet
Unlikely: The letter drawn is a vowel
Impossible: The letter drawn is a P
Certain: The paper drawn has one letter on it