Answer :
To determine which option represents an element of the sample space for first rolling a number cube and then shooting a basketball (where "X" indicates a make and "O" indicates a miss), let's break down the problem.
### Rolling a Number Cube
A standard number cube (die) has six faces, numbered from 1 to 6. When you roll the cube, the possible outcomes are:
[tex]\[ 1, 2, 3, 4, 5, 6 \][/tex]
### Shooting a Basketball
When shooting a basketball, there are two possible outcomes:
1. Make the shot (denoted by \( X \))
2. Miss the shot (denoted by \( O \))
### Combined Sample Space
An element of the combined sample space for this scenario would include:
- One outcome from rolling the number cube (1 through 6).
- One outcome from shooting the basketball (either \( X \) for making the shot or \( O \) for missing the shot).
### Evaluating the Options
Let's analyze each provided option:
Option A: \( 1, T \)
- \( 1 \): This is a possible outcome from rolling the number cube.
- \( T \): This does not relate to making or missing a basketball shot.
Option B: \( 0, 2 \)
- \( 0 \): This is not a possible outcome of rolling a number cube. The outcomes can only be between 1 and 6.
- \( 2 \): While 2 is a number that could be rolled, the pair including \( 0 \) invalidates this option.
Option C: \( 6, X \)
- \( 6 \): This is a valid outcome from rolling the number cube.
- \( X \): This indicates making the shot in basketball.
Option D: \( X, O \)
- \( X \) and \( O \): Both relate to the basketball outcome but do not include any outcome from rolling the number cube.
### Conclusion
The only option that fits the criteria of showing an element from rolling a number cube and then shooting a basketball is:
[tex]\[ \boxed{6, X} \][/tex]
Therefore, the correct answer is Option C.
### Rolling a Number Cube
A standard number cube (die) has six faces, numbered from 1 to 6. When you roll the cube, the possible outcomes are:
[tex]\[ 1, 2, 3, 4, 5, 6 \][/tex]
### Shooting a Basketball
When shooting a basketball, there are two possible outcomes:
1. Make the shot (denoted by \( X \))
2. Miss the shot (denoted by \( O \))
### Combined Sample Space
An element of the combined sample space for this scenario would include:
- One outcome from rolling the number cube (1 through 6).
- One outcome from shooting the basketball (either \( X \) for making the shot or \( O \) for missing the shot).
### Evaluating the Options
Let's analyze each provided option:
Option A: \( 1, T \)
- \( 1 \): This is a possible outcome from rolling the number cube.
- \( T \): This does not relate to making or missing a basketball shot.
Option B: \( 0, 2 \)
- \( 0 \): This is not a possible outcome of rolling a number cube. The outcomes can only be between 1 and 6.
- \( 2 \): While 2 is a number that could be rolled, the pair including \( 0 \) invalidates this option.
Option C: \( 6, X \)
- \( 6 \): This is a valid outcome from rolling the number cube.
- \( X \): This indicates making the shot in basketball.
Option D: \( X, O \)
- \( X \) and \( O \): Both relate to the basketball outcome but do not include any outcome from rolling the number cube.
### Conclusion
The only option that fits the criteria of showing an element from rolling a number cube and then shooting a basketball is:
[tex]\[ \boxed{6, X} \][/tex]
Therefore, the correct answer is Option C.
