A green number cube and a red number cube are rolled. An outcome is the pair of numbers rolled on the two different cubes. Which of the following are true? Select all that apply.
Each result is equally likely.
The sample space has 36 different outcomes.
The sample space has 11 different outcomes.
A total roll of 7 is very likely.
Each result is equally likely.
The sample space has 36 different outcomes.
A total roll of 7 is very likely.
To answer these questions, let's first understand some basics.
A number cube is a type of dice that has numbers printed on its faces, typically from 1 to 6. In this case, we have a green number cube and a red number cube.
1. Each result is equally likely:
Since these are fair and unbiased number cubes, each face has an equal probability of being rolled. So, each result is equally likely.
2. The sample space has 36 different outcomes:
To find the number of outcomes for a pair of number cubes, we multiply the number of outcomes for each individual cube. Since each cube has 6 possible outcomes, multiplying 6 by 6 gives us 36 different outcomes in total.
3. The sample space has 11 different outcomes:
This statement is not true. As calculated earlier, the sample space has 36 different outcomes, not 11.
4. A total roll of 7 is very likely:
To determine the likelihood of rolling a total of 7, we need to count the number of ways the cubes can land with a sum of 7.
We can list the pairs that result in a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). That makes a total of 6 outcomes resulting in a sum of 7.
Since each cube has 6 possible outcomes, the probability of rolling a 7 is 6/36, which simplifies to 1/6. This means that rolling a total of 7 is not "very likely."
To summarize:
- True statements: Each result is equally likely, the sample space has 36 different outcomes.
- False statements: The sample space has 11 different outcomes, a total roll of 7 is very likely.
B,D
List them to see why