Rank the three events below in increasing order of probability. For example, if you choose “A B C�, you are saying that A has the smallest chance, B has more chance than A but less chance than C, and C has the biggest chance. [If you think that some of the events have the same chance, please think again.]

A: The face with six spots shows up on fewer than 16.7% of the rolls when a die is rolled 60,000 times.
B: The face with six spots shows up on more than 16.7% of the rolls when a die is rolled 30,000 times
C: The face with six spots shows up on fewer than 16.7% of the rolls when a die is rolled 30,000 times.

...A B C
...A C B
...B A C
...B C A
...C A B
...C B A

I know ACB is wrong

BCA

thank you

Thank you , it's BCA indeed.

how to solve ??

To determine the probabilities of these events, we need to compare the proportions of rolls that result in the face with six spots.

Event A: The face with six spots shows up on fewer than 16.7% of the rolls when a die is rolled 60,000 times.
Event B: The face with six spots shows up on more than 16.7% of the rolls when a die is rolled 30,000 times.
Event C: The face with six spots shows up on fewer than 16.7% of the rolls when a die is rolled 30,000 times.

Let's break down each event and calculate the probabilities:

Event A: Rolling a die 60,000 times provides more opportunities for the face with six spots to appear. The probability of getting the face with six spots fewer than 16.7% of the time would be relatively low. Therefore, Event A has the smallest chance.

Event C: Rolling a die 30,000 times reduces the number of opportunities for the face with six spots to appear compared to Event A. Hence, the probability of getting the face with six spots fewer than 16.7% of the time would be even lower than in Event A. Thus, Event C has a smaller chance than Event A.

Event B: Rolling a die 30,000 times, but aiming for the face with six spots showing up more than 16.7% of the time, has the highest probability among the three events. This is because the target percentage for success is higher than in Events A and C, which increases the probability.

So, the correct rank from lowest to highest probability is: A C B.