Conditional Probability

Understanding Conditional Probability

• Conditional probability is the probability of an event occurring given that another event has already occurred.

• It is denoted as P(A

  B) which reads as “the probability of event A given event B”.

• The formula to calculate conditional probability is P(A

  B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring, and P(B) is the probability of event B.

Interdependence and Independence

• If the occurrence of event A affects the probability of event B, then A and B are dependent events.
• If the occurrence of event A does not affect the probability of event B, then A and B are independent events.

• For independent events, P(A

  B) = P(A), as event A’s probability isn’t influenced by event B occurring.

Applying Conditional Probability

• Tree diagrams and Venn diagrams are effective tools for illustrating and calculating conditional probabilities.
• Tree diagrams are particularly useful in clearly defining the conditional relationships between successive events.
• Conditional probability is used in many disciplines, including finance, insurance, medical research, weather forecasting, and machine learning.

Involvement in Compound Probability

• Compound probability involves combined events, for which conditional probability can provide insight.
• It includes the concept of joint probability, the probability of multiple events happening together.
• Understanding conditional probability will inform the calculation of more complex probabilities and predictions of multiple events.

Key takeaway: Conditional probability is a fundamental concept in understanding how the likelihood of one event depends on the outcome of another. This will be especially useful when dealing with complex, compound events.