To find the probability of rolling an odd number on the first roll and an even number on the second roll of a six-sided die, we can break it down into two parts.
-
Probability of rolling an odd number on the first roll:
- The odd numbers on a six-sided die (1, 2, 3, 4, 5, 6) are 1, 3, and 5.
- There are 3 odd numbers out of 6 total numbers.
- So, \( P(\text{odd on first roll}) = \frac{3}{6} = \frac{1}{2} \).
-
Probability of rolling an even number on the second roll:
- The even numbers on a six-sided die are 2, 4, and 6.
- There are 3 even numbers out of 6 total numbers.
- So, \( P(\text{even on second roll}) = \frac{3}{6} = \frac{1}{2} \).
To find the combined probability of both events happening (rolling an odd number first and then rolling an even number), we multiply the probabilities of the two independent events:
\[ P(\text{odd on first roll and even on second roll}) = P(\text{odd on first roll}) \times P(\text{even on second roll}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}. \]
So, the probability of rolling an odd number on the first roll and an even number on the second roll is \( \frac{1}{4} \).
The correct response is: Start Fraction 1 over 4 End Fraction.