Let’s analyze the problem step-by-step to find the theoretical probability of rolling a specific number, such as rolling a 3, on a fair six-sided die.
1. Understanding the Theoretical Probability:
- The theoretical probability of any specific outcome for a fair six-sided die is determined by the fact that each side has an equal chance of landing face up.
- Since a fair die has six faces, each face (or outcome) has an equal probability of [tex]\(\frac{1}{6}\)[/tex].
2. Determine the Theoretical Probability of Rolling a 3:
- There are 6 possible outcomes when rolling a fair six-sided die (i.e., 1, 2, 3, 4, 5, or 6).
- Hence, the probability of rolling any one specific number, such as a 3, is the same for each outcome.
- The theoretical probability of rolling a 3 is calculated as:
[tex]\[
P(3) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6}
\][/tex]
Given the list of possible answers:
- (a) [tex]\(\frac{1}{6}\)[/tex]
- (b) [tex]\(\frac{1}{2}\)[/tex]
- (c) [tex]\(0\)[/tex]
- (d) [tex]\(\frac{s}{6}\)[/tex]
The correct theoretical probability of rolling a 3 on a fair six-sided die matches option (a) [tex]\(\frac{1}{6}\)[/tex]. Therefore, the best option from the choices provided is:
a. [tex]\(\frac{1}{6}\)[/tex]
