Conditional Probability

Conditional probability measures the likelihood of an event occurring, given that another event has already occurred.

Formula: P(A|B) = P(A and B) / P(B)

• P(A|B): Probability of event A, given event B

• P(A and B): Probability of both events occurring

• P(B): Probability of event B

Key Characteristics:

• Depends on prior event occurrence

• Updates probability based on additional information

• Critical in statistical inference

• Used in decision-making and risk assessment

Example: Disease Testing:

• P(Disease | Positive Test)

• Incorporates test accuracy and disease prevalence

Applications:

• Medical diagnostics

• Insurance risk assessment

• Machine learning

• Weather prediction

• Financial modeling

Limitations:

• Requires accurate prior probability data

• Sensitive to initial probability estimates

• Complexity increases with multiple conditional events

Calculation Complexity:

• Simple scenarios: Straightforward calculation

• Complex scenarios: Bayesian statistical methods