Example Card: Probability of Rolling Odd Numbers on Two Dice
This Grade 8 probability example in Saxon Math Course 3, Chapter 7, walks students through calculating the probability of rolling odd numbers on two dice by listing the sample space and counting favorable outcomes. It reinforces how to apply compound probability using organized lists or tables to avoid missing or double-counting outcomes.
Key Concepts
Can you predict how often both dice will show an odd number? This taps into the key idea: using the multiplication rule for independent probability events.
Example Problem: Two number cubes (dice) are rolled. What is the probability that both rolls are odd?
Step by Step: 1. Each die has 3 odd numbers: $1, 3, 5$. 2. Probability for one die to land odd: $\frac{3}{6} = \frac{1}{2}$. 3. Since the rolls are independent, multiply their probabilities: $$P(\text{odd and odd}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$$ 4. Or, count: Each die has 3 odd choices. Total odd pairs: $3 \times 3 = 9$. Total possible pairs: $6 \times 6 = 36$. Probability: $\frac{9}{36} = \frac{1}{4}$.
Common Questions
How do you find the probability of rolling odd numbers on two dice?
List all 36 outcomes in the sample space for two dice, then count how many have odd numbers on both dice. There are 9 such outcomes (three odd numbers on each die: 1, 3, 5), so the probability is 9/36 = 1/4.
What is the sample space for rolling two dice?
The sample space for two dice has 36 equally likely outcomes, since each die has 6 faces and 6 x 6 = 36.
How do you list outcomes for compound probability?
Use an organized list, table, or tree diagram to pair every outcome from the first event with every outcome from the second event. This ensures no outcome is missed or counted twice.
What is compound probability?
Compound probability involves two or more events happening together. You find it by identifying the favorable combined outcomes and dividing by the total number of possible combined outcomes.
Where is this probability example covered in Grade 8?
This type of example is covered in Saxon Math Course 3, Chapter 7: Algebra, as part of the Grade 8 probability curriculum.