To find the probability of rolling a 4 each time on a six-sided die when rolled three times, we need to consider a few key points.
First, the probability of rolling a 4 on a single die is 1 out of 6, since there are 6 faces on the die and only one of them shows a 4. This can be expressed as:
- P(rolling a 4) = 1/6
Since we want to roll a 4 three times in a row, we need to calculate the probability of independent events. The result of one roll does not affect the others, so we can multiply the probabilities:
- P(rolling a 4 three times) = P(rolling a 4) × P(rolling a 4) × P(rolling a 4)
Putting this into the formula, we have:
- P(rolling a 4 three times) = (1/6) × (1/6) × (1/6) = (1/6)3 = 1/216
Therefore, the probability of getting a 4 each time when a die is rolled three times is 1/216.