Final answer:
One of the most important results from probability theory is known as Bayes' theorem which is used to calculate the probability that something really is the case, given evidence in favor of it.
Step-by-step explanation:
Bayes' theorem states that the probability of an event A occurring, given that B has occurred, is equal to the probability that both A and B occur divided by the probability that B occurs. In a mathematical notation, it is expressed as P(A|B) = P(A and B) / P(B).
Probability is inherently a part of many activities we engage in, from making decisions in daily life to complex scientific research.
For instance, in the study of genetics, Gregor Mendel estimated the probabilities of different traits appearing in pea plants, which helped him to predict the outcomes of genetic crosses.
In finance, probabilities can be used to determine the expected rate of return on investments. As the number of trials in a probability experiment increases, the law of large numbers tells us that the empirical results will converge on the theoretical probability.