Question

A number cube is rolled and a letter is selected from the word GIRAFFE. Find the probability.
P (4 and F)
A
121\frac{1}{21}
21
1
​

B
16\frac{1}{6}
6
1
​

C
27\frac{2}{7}
7
2
​

D
142\frac{1}{42}
42
1
​

Answer 1

To solve for the probability \( P(4 \text{ and } F) \), we need to break this down into two components: rolling a 4 on a number cube (die) and selecting the letter 'F' from the word "GIRAFFE".

1. **Rolling a 4 on a cube:**
- A standard number cube has 6 faces numbered from 1 to 6.
- The probability of rolling a 4 is:
\[
P(4) = \frac{1}{6}
\]

2. **Selecting 'F' from the word "GIRAFFE":**
- The word "GIRAFFE" has 7 letters, and the letter 'F' appears 2 times.
- The probability of selecting 'F' is:
\[
P(F) = \frac{2}{7}
\]

3. **Calculating the combined probability:**
- Since the rolling of the die and selecting a letter are independent events, the combined probability is the product of the two individual probabilities:
\[
P(4 \text{ and } F) = P(4) \times P(F) = \frac{1}{6} \times \frac{2}{7} = \frac{2}{42} = \frac{1}{21}
\]

Thus, the probability \( P(4 \text{ and } F) \) is \( \frac{1}{21} \).

**Answer: A \( \frac{1}{21} \)**