Final answer:
You are interested in the money won or lost when you roll a die, and the random variable X represents this net gain or loss. The probability of rolling a 5 or 6 on a fair die is 0.3333, and with a large number of rolls, about one-third should be a 5 or 6.
Step-by-step explanation:
You are ultimately interested in the money you win or lose when you roll the die based on the defined outcomes and corresponding monetary values. The random variable X can be defined as the net gain or loss of money as a result of one roll of the die.
Suppose you roll a fair, six-sided die with faces numbered {1, 2, 3, 4, 5, 6}. If we define event E as rolling a number that is at least five, there are two outcomes which are {5, 6}, and the probability of event E, P(E), is 2 out of 6, or approximately 0.3333 when rounded to four decimal places.
If you repeatedly roll the die, it is statistically plausible to expect about one-third of the rolls to result in a five or a six over a large number of trials.
In a collaborative exercise, if you roll one fair die 20 times, you would record the frequency of each number (1 through 6) and compare the relative frequency to the theoretical probability of each outcome, which should be approximately 0.1667 for each face, assuming that the die is perfectly fair and random.