Final answer:
Cassie is most likely to roll each number around 50 times when a fair six-sided die is rolled 300 times, due to each side having an equal probability of 1/6.
Step-by-step explanation:
When Cassie rolls a fair number cube with 6 faces labeled 1 through 6 a total of 300 times, it is most likely that each number would appear approximately an equal number of times. This outcome is expected because each face has an equal probability of landing face up on any given roll.
For a fair die, the probability of rolling any one of the numbers, 1 through 6, is ⅖ or approximately 16.67%. If she rolls the die 300 times, we expect each number to appear close to 300 × 16.67% = 50 times, because 300 rolls is a large enough number to approach the expected frequency based on the probability.
Conducting a Collaborative Exercise:
In a classroom setting, students might perform a collaborative exercise by rolling dice multiple times to record the frequencies of each outcome, which will often closely mimic the theoretical probabilities.