Final answer:
Physical and logical probabilities are considered separate in mathematics because they represent different concepts and are calculated using different methods.
Step-by-step explanation:
In mathematics, physical and logical probabilities are considered separate because they represent different concepts and are calculated using different methods.
Physical probability refers to the likelihood of an event occurring in the real world based on physical observations and measurements. It is calculated using empirical data and can be estimated by conducting experiments or making observations.
Logical probability, on the other hand, is based on logical reasoning and mathematical models. It is calculated using theoretical probabilities and can be used to predict the likelihood of an event occurring based on assumptions and mathematical principles.
For example, if we toss a fair coin, the physical probability of getting heads or tails is 1/2 based on empirical observations. However, the logical probability can be calculated using mathematical principles, where we consider all possible outcomes and divide the favorable outcomes by the total number of outcomes.