Final answer:
The probability of rolling a 1 on a six-sided die is 1/6. For all six dice to land on 1, the probability is (1/6)^6. Comparing probabilities for three or four dice landing on 1 requires using binomial probability formulas.
Step-by-step explanation:
The probability of a cube (a six-sided die) rolling a 1 facing up is 1/6, because there is only one face with a 1 on it and six possible outcomes. This is assuming the die is fair, meaning all outcomes are equally likely. To find the probability that all six dice show a 1, you would multiply the probability of a single die showing a 1 (1/6) by itself six times, because each die is independent of the others, which results in (1/6)^6.
When comparing the likelihood of three or four dice showing a 1, you would calculate the probabilities separately, using binomial probability formulas. For three dice showing a 1, the calculation is C(6,3)*(1/6)^3*(5/6)^3, and for four dice showing a 1, the calculation is C(6,4)*(1/6)^4*(5/6)^2. Whichever outcome has the higher probability is the more likely event.