Answer :
To determine the probability of randomly drawing a consonant from the set of letters that spell out "MATHCLUB," follow these steps:
1. Identify the total number of letters:
- The set of letters is M, A, T, H, C, L, U, and B.
- Counting these letters, we have a total of 8 letters.
2. Identify the vowels in the set:
- The vowels from the given letters are A and U.
3. Identify the consonants in the list:
- By excluding the vowels from the total set of letters, the remaining letters are consonants.
- The consonants are M, T, H, C, L, and B.
4. Determine the total number of consonants:
- Counting the consonants, we have 6 consonants.
5. Calculate the probability of drawing a consonant:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this case, the favorable outcomes are the consonants, and the possible outcomes are all the letters.
- Therefore, the probability of drawing a consonant is given by:
[tex]\[ \text{Probability} = \frac{\text{Number of consonants}}{\text{Total number of letters}} = \frac{6}{8} \][/tex]
- This can be simplified to:
[tex]\[ \frac{6}{8} = \frac{3}{4} = 0.75 \][/tex]
Hence, the probability of randomly drawing a consonant from the set of letters is [tex]\(\frac{6}{8}\)[/tex].
1. Identify the total number of letters:
- The set of letters is M, A, T, H, C, L, U, and B.
- Counting these letters, we have a total of 8 letters.
2. Identify the vowels in the set:
- The vowels from the given letters are A and U.
3. Identify the consonants in the list:
- By excluding the vowels from the total set of letters, the remaining letters are consonants.
- The consonants are M, T, H, C, L, and B.
4. Determine the total number of consonants:
- Counting the consonants, we have 6 consonants.
5. Calculate the probability of drawing a consonant:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this case, the favorable outcomes are the consonants, and the possible outcomes are all the letters.
- Therefore, the probability of drawing a consonant is given by:
[tex]\[ \text{Probability} = \frac{\text{Number of consonants}}{\text{Total number of letters}} = \frac{6}{8} \][/tex]
- This can be simplified to:
[tex]\[ \frac{6}{8} = \frac{3}{4} = 0.75 \][/tex]
Hence, the probability of randomly drawing a consonant from the set of letters is [tex]\(\frac{6}{8}\)[/tex].
