Final answer:
To find the theoretical probability of rolling a 3 on a fair six-sided die, divide the number of favorable outcomes (1) by the total number of possible outcomes (6), resulting in a probability of 1/6 or approximately 0.1667.
Step-by-step explanation:
The student has asked about the theoretical probability of rolling a 3 on a fair number cube, which is a six-sided die. The sample space for a single roll of a six-sided dice is {1, 2, 3, 4, 5, 6}. Since the die is fair, each outcome has an equal chance of occurring. Therefore, the probability of any specific outcome, such as rolling a 3, is 1 divided by the total number of outcomes.
The calculation is straightforward:
- Determine the total number of possible outcomes (6).
- Identify the number of outcomes that result in the event occurring (1, which is rolling a 3).
- Divide the number of events by the total number of outcomes to get the probability.
Therefore, P(rolling a 3) = 1/6 ≈ 0.1667 (rounded to four decimal places).