Question
The table below shows all of the possible outcomes for rolling two six-sided number cubes.
A table with 36 possible outcomes. There are 9 desired outcomes.
What is the probability of rolling an even number first and an odd number second?
StartFraction 1 over 9 EndFraction
StartFraction 1 over 6 EndFraction
One-fourth
One-half
A table with 36 possible outcomes. There are 9 desired outcomes.
What is the probability of rolling an even number first and an odd number second?
StartFraction 1 over 9 EndFraction
StartFraction 1 over 6 EndFraction
One-fourth
One-half
Answers
GPT-4o mini
To find the probability of rolling an even number first and an odd number second when rolling two six-sided dice, we first identify the even and odd numbers on a die.
Even numbers on a six-sided die: 2, 4, 6 (3 options)
Odd numbers on a six-sided die: 1, 3, 5 (3 options)
1. **Calculating Desired Outcomes:**
- For the first die (even), there are 3 choices (2, 4, or 6).
- For the second die (odd), there are also 3 choices (1, 3, or 5).
The total number of desired outcomes for this specific situation (even first, odd second) is:
\[
3 \text{ (even choices)} \times 3 \text{ (odd choices)} = 9 \text{ desired outcomes}
\]
2. **Calculating Total Outcomes:**
The total number of outcomes when rolling two six-sided dice is:
\[
6 \text{ (from first die)} \times 6 \text{ (from second die)} = 36 \text{ total outcomes}
\]
3. **Calculating Probability:**
The probability \( P \) of rolling an even number first and an odd number second is given by the ratio of the number of desired outcomes to the total number of outcomes:
\[
P = \frac{\text{Number of desired outcomes}}{\text{Total outcomes}} = \frac{9}{36} = \frac{1}{4}
\]
Thus, the probability of rolling an even number first and an odd number second is:
\[
\boxed{\frac{1}{4}}
\]
Even numbers on a six-sided die: 2, 4, 6 (3 options)
Odd numbers on a six-sided die: 1, 3, 5 (3 options)
1. **Calculating Desired Outcomes:**
- For the first die (even), there are 3 choices (2, 4, or 6).
- For the second die (odd), there are also 3 choices (1, 3, or 5).
The total number of desired outcomes for this specific situation (even first, odd second) is:
\[
3 \text{ (even choices)} \times 3 \text{ (odd choices)} = 9 \text{ desired outcomes}
\]
2. **Calculating Total Outcomes:**
The total number of outcomes when rolling two six-sided dice is:
\[
6 \text{ (from first die)} \times 6 \text{ (from second die)} = 36 \text{ total outcomes}
\]
3. **Calculating Probability:**
The probability \( P \) of rolling an even number first and an odd number second is given by the ratio of the number of desired outcomes to the total number of outcomes:
\[
P = \frac{\text{Number of desired outcomes}}{\text{Total outcomes}} = \frac{9}{36} = \frac{1}{4}
\]
Thus, the probability of rolling an even number first and an odd number second is:
\[
\boxed{\frac{1}{4}}
\]