Theoretical Probability

Theoretical probability is the likelihood of an event occurring based on all the possible outcomes. It is calculated by determining the ratio of the number of favorable outcomes to the total number of possible outcomes.

Formula for Theoretical Probability

The formula for theoretical probability is:

P(E) = Number of favorable outcomes / Total number of possible outcomes

Where:

P(E) = Theoretical probability of event E
Number of favorable outcomes = The number of outcomes that make the event favorable
Total number of possible outcomes = The total number of outcomes in the sample space

Example

Let's say we have a standard six-sided die. The theoretical probability of rolling a 3 is:

P(rolling a 3) = 1 (there is 1 favorable outcome - rolling a 3) / 6 (there are 6 possible outcomes when rolling a die)

So, the theoretical probability of rolling a 3 is 1/6 or approximately 0.1667.

Conclusion

Theoretical probability provides a way to predict the likelihood of an event occurring based on the underlying principles of probability. It is an important concept in mathematics and is used in various real-life situations to make informed decisions.