If you roll three regular dice, what is the probability that at least one of the numbers is more than three?
Solution:
There are six possible outcomes for rolling a dice. Three of them are more than three. Therefore, for each dice, the probability that the number rolled is more than three is 1/2. The probability that it is three or less is also 1/2.
Because the chance of the number being more than three is the same as the chance of it being three or less, we can just list and count all the possibilities for the three dice. In the list below, 3 stands for 3 or less, while 4 stands for 4 or more.
333
334
343
344
433
434
443
444
There are eight possible outcomes, of which seven include at least one number greater than three. Therefore, the probability of rolling at least one number greater than three when rolling three dice is 7/8