Conditional Probability

Conditional Probability

Definition:

• Meaning: Probability of event A occurring given that event B has already occurred.
• Formula: P(A∣B) = P(A∩B)/P(B)

Application in Real Experiments:

• Civil Engineering Example: Determining the probability of cube strength given cube density falls within specified ranges.
• Figure 2.15 Explanation:
  • Visual Representation: Using Venn diagrams to illustrate conditional probability.
  • Example: Given 100 trips between places X and Y, where 50 trips are by car, 25 by bus, and 25 by local train, calculate the probability of choosing the bus given that public transportation is chosen.

Key Points:

• Dependence: Conditional probability shows how one event affects the likelihood of another.
• Calculation: Based on the intersection of events and their individual probabilities.
• Applications: Widely used in fields like engineering, medicine, and finance for decision-making and risk assessment.

Usage: Essential for understanding relationships between events and making informed predictions based on observed data.