Question
A number cube is rolled and a letter is selected from the word GIRAFFE. Find the probability.
P (4 and F)
P (4 and F)
Answers
GPT-4o mini
To find the probability of rolling a 4 on a number cube and selecting the letter F from the word "GIRAFFE," we first need to determine the probability of each event separately and then multiply them to find the combined probability.
1. **Probability of rolling a 4 on a number cube**:
A number cube (or die) has 6 faces, numbered 1 through 6. The probability of rolling any specific number (including 4) is:
\[
P(\text{rolling a 4}) = \frac{1}{6}
\]
2. **Probability of selecting the letter F from "GIRAFFE"**:
The word "GIRAFFE" consists of 7 letters: G, I, R, A, F, F, E. The letter F appears twice. Therefore, the probability of selecting the letter F is:
\[
P(\text{selecting F}) = \frac{\text{number of F's}}{\text{total letters}} = \frac{2}{7}
\]
3. **Combined probability**:
Since these two events (rolling the die and selecting a letter) are independent, we can multiply their probabilities:
\[
P(4 \text{ and } F) = P(\text{rolling a 4}) \times P(\text{selecting F}) = \frac{1}{6} \times \frac{2}{7} = \frac{2}{42} = \frac{1}{21}
\]
Thus, the probability \( P(4 \text{ and } F) \) is \( \frac{1}{21} \).
1. **Probability of rolling a 4 on a number cube**:
A number cube (or die) has 6 faces, numbered 1 through 6. The probability of rolling any specific number (including 4) is:
\[
P(\text{rolling a 4}) = \frac{1}{6}
\]
2. **Probability of selecting the letter F from "GIRAFFE"**:
The word "GIRAFFE" consists of 7 letters: G, I, R, A, F, F, E. The letter F appears twice. Therefore, the probability of selecting the letter F is:
\[
P(\text{selecting F}) = \frac{\text{number of F's}}{\text{total letters}} = \frac{2}{7}
\]
3. **Combined probability**:
Since these two events (rolling the die and selecting a letter) are independent, we can multiply their probabilities:
\[
P(4 \text{ and } F) = P(\text{rolling a 4}) \times P(\text{selecting F}) = \frac{1}{6} \times \frac{2}{7} = \frac{2}{42} = \frac{1}{21}
\]
Thus, the probability \( P(4 \text{ and } F) \) is \( \frac{1}{21} \).