You roll five fair, six-sided dice, all at the same time. In that one roll, what is the probability of getting five of the same number?
Source: NCTM Mathematics Teacher, September 2006
When you roll five dice at the same time, possible numbers from through can come up on each of the five dice. The number of possible outcomes = . There are possible ways the five dice come up with the same number: . The probability of getting five of the same number in one roll = .
Suppose the event occurs on a roll. Since the number on the first dice is independent of the number on the second dice, etc., the probability of the event . The probability of getting five of the same number in one roll = .