Mack rolls a 15-sided cube 45 times, what would you predict the probability to be of Mack's rolling a number less than 5?

The concept of a 15 sided cube startles me.

Did you make this question up yourself?

No, it's a question on a 7th grade Skills Review

You are right; there's no way a 15-sided die could be fair. Even if the area of each face is the same, the angles cannot all be equal, since there is no regular 15-hedron.

Perhaps they want us to assume it is possible.

4 out of the 15 sides are less than 5
so
about 4/15 in each roll
so in each roll the probability of NOT getting less than 5 is 11/15
so the probability of NEVER getting less than 5 is (11/15)^45
so our answer is
1 - (11/15)^45

which is about
1 - 8.7^-7

which is so close to one that you can count on it :)

To find the probability of Mack rolling a number less than 5, we need to determine the number of favorable outcomes (i.e., rolling a number less than 5) and divide it by the total number of possible outcomes.

First, let's determine the number of favorable outcomes. Since Mack is rolling a 15-sided cube, we need to count the number of sides with a number less than 5. In this case, the numbers less than 5 are {1, 2, 3, 4}. So, there are 4 favorable outcomes.

Next, we determine the total number of possible outcomes. Mack rolls the 15-sided cube 45 times. Since each roll is an independent event, we can multiply the possibilities for each roll. In this case, there are 15 possible outcomes for each roll, so the total number of possible outcomes is 15^45.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
= 4 / (15^45)

Unfortunately, calculating the exact probability in this case is not feasible due to the large number involved (15^45). However, we can still estimate the probability. Since 4 is significantly smaller than 15^45, the probability is expected to be a very small value close to 0.