Final answer:
The possible values of X, the random variable for a fair die's face value, are {1, 2, 3, 4, 5, 6}. The nature of X changes depending on the question's context such as the net monetary outcome of a die roll or the number of dice showing a particular face.
Step-by-step explanation:
If X is a random variable representing the face value on the throw of a fair die, the possible values that X can take are the numbers on the faces of the die. Since a standard six-sided die has six faces with the numbers 1 through 6 on them, the possible values of X are {1, 2, 3, 4, 5, 6}. So, the correct answer to the question is c. {1, 2, 3, 4, 5, 6}.
Now, looking at the provided scenarios and examples:
- 74. When you are offered a deal based on the roll of a die with different monetary outcomes, you are ultimately interested in the money you win or lose, which would be determined by the value of the roll. Thus, in this scenario, X could be defined as the random variable representing the net monetary outcome of rolling a die, based on the stipulated rules.
- 94. If six different colored dice are rolled, and the number of dice that show a one is of interest, then X can be defined as the random variable representing the number of dice that land on one.
- In the final example, the sample space of rolling one fair six-sided die is {1, 2, 3, 4, 5, 6}. If event E represents rolling a number at least five, then the probability P(E) is 2 out of 6, which simplifies to 1/3 since there are two favorable outcomes out of six possible outcomes.