A player rolls four 20-sided dice, takes the lowest value, ignores the rest. What is the probability of this value at least 7?


I’m designing a tabletop game, and I need to figure out how to calculate a few probabilities:

  1. Roll 3 20-sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or higher?
    1. Roll 4 20-sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or higher?
    1. Roll 3 20-sided dice, take the lowest value. What is the probability of it being 7 or higher? 15 or higher?
    1. Roll 4 20-sided dice, take the lowest value. What is the probability of it being 7 or higher? 15 or higher?

How can I do this? Could you explain to me how this works, or even better – give me a simple formula?