Well, the question is more complex than it seems at first glance, but you'll soon see that the answer isn't that scary! It's all about maths and statistics. First of all, we have to determine what kind of dice roll probability we want to find. We can distinguish a few which you can find in this dice probability calculator. Before we make any calculations, let's define some variables which are used in the formulas. n - the number of dice, s - the number of an individual die faces, p - the probability of rolling any value from a die, and P - the overall probability for the problem. There is a simple relationship - p = 1/s, so the probability of getting 7 on a 10 sided die is twice that of on a 20 sided die.
In our example we have n = 7, p = 1/12, r = 2, nCr = 21, so the final result is: P(X=2) = 21 * (1/12)² * (11/12)⁵ = 0.09439, or P(X=2) = 9.439% as a percentage.
The first die is already 6, so to satisfy the condition that sum is greater than 8, the second die must be {3,4,5,6}. We have 4 events that satisfy the condition, and 6 possible events (getting any number from 1 to 6). So the probability is "\\displaystyle P(A) = \\frac{4}{6} = \\frac{2}{3}" Answer: 2/3 |