The probability of rolling a specific number on a standard six-sided die is 1/6 because there are six equally likely outcomes (the numbers 1 through 6) and only one of them is a 4.
When rolling the die multiple times, the events are independent. This means the outcome of one roll does not affect the outcome of another. To find the probability of multiple independent events occurring together, you multiply the probabilities of each event.
In this case, the probability of rolling a 4 on the first roll is 1/6, on the second roll is also 1/6, and on the third roll is again 1/6.
Therefore, the total probability of rolling a 4 on all three rolls can be calculated as follows:
Probability = (1/6) * (1/6) * (1/6) = (1/6)3 = 1/216So, the probability of rolling a 4 each time when a die is rolled three times is 1/216.