To calculate the Bayesian Probability:
\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \]
Bayesian probability is a theory in statistics that provides a mathematical framework for updating probabilities based on new evidence. Named after Thomas Bayes, it interprets probability as a measure of belief or confidence in an event occurring, which can be updated as new data or information becomes available. This approach contrasts with classical or frequentist probability, which interprets probability as the long-run frequency of events. Bayesian probability is widely used in machine learning, data analysis, and statistical inference.
Let's assume the following values:
Step 1: Multiply P(B|A) by P(A):
\[ P(B|A) \times P(A) = 0.8 \times 0.5 = 0.4 \]
Step 2: Divide the result by P(B):
\[ P(A|B) = \frac{0.4}{0.6} \approx 0.67 \]
So, the Bayesian Probability \( P(A|B) \) is approximately 0.67.
