When given a set of cards lying face down that spell M, A, T, H, F, A, N, determine the probability of randomly drawing a consonant.

six halves
six sevenths
five sevenths
two sevenths

To determine the probability of randomly drawing a consonant from the set of cards that spell "MATHFAN," let's break down the problem:

1. **Identify the consonants in the word "MATHFAN":**
   - The consonants are: M, T, H, F, N.

2. **Count the number of consonants:**
   - There are 5 consonants (M, T, H, F, N).

3. **Count the total number of cards (letters):**
   - The total number of letters in "MATHFAN" is 7.

4. **Calculate the probability:**
   - Probability of drawing a consonant \( P(\text{consonant}) \) = \( \frac{\text{Number of consonants}}{\text{Total number of cards}} = \frac{5}{7} \).

The correct answer is **five sevenths**.

Would you like further details or have any other questions?

Here are some related questions:

1. What is the probability of drawing a vowel from the same set of cards?
2. If two cards are drawn randomly, what is the probability that both are consonants?
3. How does the probability change if one card is removed after drawing a consonant?
4. What if the cards are reshuffled after each draw? How would that affect the probability of drawing a consonant?
5. How many different ways can you arrange the letters in "MATHFAN"?
6. If the letters are drawn one at a time, what is the probability that the first letter is a vowel?
7. How does the probability of drawing a consonant compare to drawing a vowel?
8. What is the probability of drawing either the letter M or N?

**Tip:** When dealing with probability questions, always identify the total possible outcomes and the favorable outcomes to calculate the probability correctly.

Calculate the probability of randomly drawing a consonant from the set of cards spelling MATHFAN. Understand the basic concept of probability and its application in card drawing scenarios. Suitable for students in Grades 6-8.

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