Final answer:
While the first part of the student's question on assessment chances does not align with a mathematical concept, information on probabilities involving dice and statistics about colleges with online offerings are discussed, including expected outcomes, binomial probabilities, and binomial distribution.
Step-by-step explanation:
Regarding the question about the number of chances to pass a level assessment, this seems like a general education query and does not directly pertain to a math problem. However, since the latter part of the student's query involves probability and statistics, we can address these:
d. On average, how many dice would you expect to show a one?
If you are rolling six dice, the probability of any one die showing a one is 1/6. Therefore, on average, you would expect one out of every six dice to show a one, so for six dice, you would expect to see one die showing a one on average (6 * (1/6)).
e. Find the probability that all six dice show a one.
The probability of rolling a one on a single die is 1/6. Since each die is independent, the probability of all six dice showing a one is (1/6)^6.
f. Is it more likely that three or that four dice will show a one? Use numbers to justify your answer numerically.
To determine which event is more likely, we would use the binomial probability formula which takes into account the number of trials (n), the number of successes (x), the probability of success (p), and the probability of failure (q). For three dice showing a one, the combination would be calculated as C(n=6, x=3) * p^3 * q^3. For four dice, it would be C(n=6, x=4) * p^4 * q^2. You would need to calculate these two probabilities and compare them to find out which is more likely.
When discussing the percentage of large colleges and universities with online offerings, it's noted that more than 96 percent of the very largest institutions offer some form of distance learning. If you randomly pick 13 such institutions, the probability that a given institution offers distance learning courses would be 0.96. The number of these 13 institutions that offer distance learning courses can be examined through a binomial distribution, where each institution is a trial with a probability of success (offering distance learning) of 0.96.