00:01
So for this problem, a fair six -sided die is rolled five times, and we want to calculate the probability that all five rolls give us three.
00:12
So if it's a fair die, that means there is an equal probability to roll any given number from one to six.
00:20
So the probability, let's say the probability of getting a three, i'll say roll three, is equal to, one in six.
00:35
And since each dice rule can be assumed to be independent, that is the role doesn't depend on the previous rule, we can just multiply this probability for each rule.
00:46
So if we roll the die the die five times, then it's a one in six chance on the first rule times a one and six chance on the second, and then a one and six chance on the third and on the fourth and on the fifth, which is just one over six to the power of five since we're rolling five times.
01:06
So we can see what six to the power five is and then we'll have our answer as a fraction...
