Final answer:
The theoretical probability of rolling a 2 on a fair, six-sided die is 1/6, since there is one favorable outcome (rolling a 2) out of six possible outcomes (1, 2, 3, 4, 5, 6).
Step-by-step explanation:
Theoretical Probability of Rolling a Two
To determine the theoretical probability of rolling a 2 on a fair, six-sided die, you need to consider the total number of possible outcomes and the number of outcomes that result in a 2. A standard six-sided die has the numbers 1 through 6 on its faces, so the sample space S is {1, 2, 3, 4, 5, 6}. The event of rolling a 2 is just one outcome, which we can denote as E = {2}.
To calculate the theoretical probability of event E (rolling a 2), you divide the number of favorable outcomes by the total number of possible outcomes in sample space S. There is only one favorable outcome, the number 2, out of a total of six possible outcomes.
The formula for theoretical probability is P(E) = Number of favorable outcomes / Total number of possible outcomes.
In this case, P(E) = 1/6. Therefore, the theoretical probability of rolling a 2 on a six-sided die is approximately 0.1667 (when rounded to four decimal places).