Question

What is theoretical probability definition and example

Answer 1

**Theoretical Probability** is the probability calculated based on the possible outcomes of an event in a perfect world where all outcomes are equally likely. It is determined through reasoning and mathematical calculation rather than experimental or empirical means.

**Definition:**
Theoretical probability is defined as:
\[
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]
where \( P(E) \) is the probability of the event \( E \).

**Example:**
Suppose you have a standard six-sided die. The possible outcomes when rolling the die are: 1, 2, 3, 4, 5, and 6.

If we want to calculate the probability of rolling a 4, we can denote the event \( E \) as "rolling a 4".

- **Number of favorable outcomes for event \( E \)**: There is 1 favorable outcome (the outcome of rolling a 4).
- **Total number of possible outcomes when rolling a die**: There are 6 possible outcomes (1, 2, 3, 4, 5, 6).

Using the formula for theoretical probability:
\[
P(\text{rolling a 4}) = \frac{1}{6}
\]

So, the theoretical probability of rolling a 4 on a six-sided die is \( \frac{1}{6} \).