Question

Theoretical Probabilities of Repeated Events Practice
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Question
A traditional number cube is rolled twice. What is the probability that the first roll lands on an even number, and the second roll lands on an odd number? Express your answer as a simplified fraction.(1 point)

Answer 1

A traditional number cube (or die) has 6 faces, numbered from 1 to 6. The even numbers on the cube are 2, 4, and 6, while the odd numbers are 1, 3, and 5.

1. **Calculating the probability of rolling an even number on the first roll:**
- There are 3 even numbers (2, 4, 6) out of 6 total numbers.
- So, \( P(\text{even}) = \frac{3}{6} = \frac{1}{2} \).

2. **Calculating the probability of rolling an odd number on the second roll:**
- There are 3 odd numbers (1, 3, 5) out of 6 total numbers.
- So, \( P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \).

3. **Finding the overall probability:**
- Since the rolls are independent events, we can multiply the probabilities:
\[
P(\text{even on first roll and odd on second roll}) = P(\text{even}) \times P(\text{odd}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.
\]

Thus, the probability that the first roll lands on an even number and the second roll lands on an odd number is \(\frac{1}{4}\).