The Table Shows The Outcomes Of Rolling Two Number Cubes At The Same Time And Finding The Product Of The Two Numbers. If Abby Rolls Two Number Cubes Three Hundred Times, About How Many Times Would She Expect A Product Greater Than 10? Enter Your Answer
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Introduction
In this article, we will explore the outcomes of rolling two number cubes at the same time and finding the product of the two numbers. We will use a table to display the possible outcomes and then use this information to determine how many times Abby would expect a product greater than 10 if she rolls two number cubes three hundred times.
Understanding the Table
The table below shows the possible outcomes of rolling two number cubes and finding the product of the two numbers.
| Cube 1 | Cube 2 | Product |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 2 | 2 |
| 1 | 3 | 3 |
| 1 | 4 | 4 |
| 1 | 5 | 5 |
| 1 | 6 | 6 |
| 2 | 1 | 2 |
| 2 | 2 | 4 |
| 2 | 3 | 6 |
| 2 | 4 | 8 |
| 2 | 5 | 10 |
| 2 | 6 | 12 |
| 3 | 1 | 3 |
| 3 | 2 | 6 |
| 3 | 3 | 9 |
| 3 | 4 | 12 |
| 3 | 5 | 15 |
| 3 | 6 | 18 |
| 4 | 1 | 4 |
| 4 | 2 | 8 |
| 4 | 3 | 12 |
| 4 | 4 | 16 |
| 4 | 5 | 20 |
| 4 | 6 | 24 |
| 5 | 1 | 5 |
| 5 | 2 | 10 |
| 5 | 3 | 15 |
| 5 | 4 | 20 |
| 5 | 5 | 25 |
| 5 | 6 | 30 |
| 6 | 1 | 6 |
| 6 | 2 | 12 |
| 6 | 3 | 18 |
| 6 | 4 | 24 |
| 6 | 5 | 30 |
| 6 | 6 | 36 |
Analyzing the Table
From the table, we can see that the possible products range from 1 to 36. We are interested in finding the number of times a product greater than 10 is obtained.
Calculating the Probability
To calculate the probability of obtaining a product greater than 10, we need to count the number of outcomes where the product is greater than 10 and divide it by the total number of outcomes.
From the table, we can see that the following outcomes have a product greater than 10:
- 2 x 6 = 12
- 3 x 4 = 12
- 3 x 5 = 15
- 3 x 6 = 18
- 4 x 5 = 20
- 4 x 6 = 24
- 5 x 4 = 20
- 5 x 5 = 25
- 5 x 6 = 30
- 6 x 5 = 30
- 6 x 6 = 36
There are 11 outcomes where the product is greater than 10.
Determining the Expected Number of Times
Since Abby rolls two number cubes three hundred times, we can use the probability of obtaining a product greater than 10 to determine the expected number of times.
The probability of obtaining a product greater than 10 is 11/36.
To calculate the expected number of times, we multiply the probability by the total number of rolls:
Expected number of times = (11/36) x 300
Expected number of times ≈ 91.67
Since we cannot have a fraction of a time, we round down to the nearest whole number.
Expected number of times ≈ 91
Conclusion
In this article, we used a table to display the possible outcomes of rolling two number cubes and finding the product of the two numbers. We then used this information to determine how many times Abby would expect a product greater than 10 if she rolls two number cubes three hundred times. The expected number of times is approximately 91.
Final Answer
The final answer is 91.
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Q: What is the probability of obtaining a product greater than 10 when rolling two number cubes?
A: The probability of obtaining a product greater than 10 is 11/36.
Q: How many times would I expect to obtain a product greater than 10 if I roll two number cubes three hundred times?
A: You would expect to obtain a product greater than 10 approximately 91 times.
Q: What is the expected number of times I would obtain a product of 1 when rolling two number cubes?
A: Since there is only one outcome where the product is 1 (1 x 1), the expected number of times you would obtain a product of 1 is 1/36.
Q: How many times would I expect to obtain a product of 36 when rolling two number cubes?
A: Since there is only one outcome where the product is 36 (6 x 6), the expected number of times you would obtain a product of 36 is 1/36.
Q: What is the probability of obtaining a product of 12 when rolling two number cubes?
A: There are two outcomes where the product is 12 (2 x 6 and 3 x 4). Therefore, the probability of obtaining a product of 12 is 2/36.
Q: How many times would I expect to obtain a product of 15 when rolling two number cubes?
A: There is only one outcome where the product is 15 (3 x 5). Therefore, the expected number of times you would obtain a product of 15 is 1/36.
Q: What is the probability of obtaining a product of 20 when rolling two number cubes?
A: There are two outcomes where the product is 20 (4 x 5 and 5 x 4). Therefore, the probability of obtaining a product of 20 is 2/36.
Q: How many times would I expect to obtain a product of 30 when rolling two number cubes?
A: There are two outcomes where the product is 30 (5 x 6 and 6 x 5). Therefore, the expected number of times you would obtain a product of 30 is 2/36.
Q: What is the probability of obtaining a product of 36 when rolling two number cubes?
A: There is only one outcome where the product is 36 (6 x 6). Therefore, the probability of obtaining a product of 36 is 1/36.
Q: Can I use this information to determine the expected number of times I would obtain a product of a specific number?
A: Yes, you can use the probability of obtaining a product of a specific number to determine the expected number of times. Simply multiply the probability by the total number of rolls.
Q: How can I use this information in real-life situations?
A: This information can be used in a variety of real-life situations, such as:
- Determining the expected number of times a product will be greater than a certain value in a manufacturing process.
- Calculating the probability of obtaining a specific product in a game or simulation.
- Understanding the expected outcomes of a random event.
Q: Are there any limitations to this information?
A: Yes, there are several limitations to this information. For example:
- This information assumes that the number cubes are fair and unbiased.
- This information assumes that the number cubes are rolled independently.
- This information does not take into account any external factors that may affect the outcome of the rolls.
Q: Can I use this information to determine the expected number of times I would obtain a product of a specific number in a specific situation?
A: Yes, you can use this information to determine the expected number of times you would obtain a product of a specific number in a specific situation. However, you will need to take into account any external factors that may affect the outcome of the rolls.