ISDS Chapter 4 Flashcards

Probability Concepts

• Classical Probability: Determined when outcomes are equally likely, e.g., flipping a fair coin results in a 50% chance of tails.
• Subjective Probability: Based on personal belief or assessment, such as estimating a 90% chance of achieving straight A's.
• Empirical Probability: Derived from observed data or experimental outcomes, e.g., reporting a 50% chance of a train being on time based on past experiences.

Probability Calculations

• Probability of a Single Event (P(D)): For five equally likely events, the probability of any single event (e.g., P(D)) is 0.20.
• Complementary Events: The probability of the complement of an event (e.g., P(B^c)) is calculated by subtracting the probability of the event from 1, resulting in 0.80 for P(B^c).
• Union of Events (P(A U C U E)): The probability of the union of several events can be calculated by summing their individual probabilities; e.g., P(A) + P(C) + P(E) results in 0.60.

Advanced Probability

• Calculating Joint Probability (P(A ∩ B)): The joint probability of two events can be derived using conditional probability; for example, P(A ∩ B) = P(A | B) * P(B) resulting in 0.081.
• Calculating Union (P(A U B)): The combined probability of two events is calculated using P(A) + P(B) − P(A ∩ B), yielding 0.709.
• Conditional Probability (P(B | A)): Conditional probability shows the likelihood of an event given another event has occurred, calculated as P(A ∩ B) / P(A), equating to 0.142.

Independence and Mutual Exclusivity

• Independent Events: Events A and B are independent if P(A | B) equals P(A); in this case, they are not independent.
• Mutually Exclusive Events: Events that cannot happen simultaneously have a joint probability of zero; however, A and B are not mutually exclusive since P(A ∩ B) is not zero.

Probability of Non-occurrence

• Calculating neither A nor B Occurring: To calculate the probability that neither event occurs, use the formula P((A U B)^c) = 1 − P(A U B), resulting in 0.36.

Stock Price Probabilities

• At least one Event Occurring: The probability of at least one stock rising in price is found by calculating P(A U B) = P(A) + P(B) − P(A ∩ B), yielding 0.77.

Bond Default Probabilities

• Probability of Neither Bond Defaulting: To find the likelihood that neither bond defaults, use P((A U B)^c) = 1 − P(A U B), resulting in 0.10.
• Probability of at least One Bond Defaulting: The combined probability of either bond defaulting can be calculated similarly, yielding a probability of 0.90.

Summary of Probability Types

• Events classified as empirical, classical, or subjective variations affects their interpretation and usage in practical applications.
• Understanding complements, joint probabilities, and conditional relationships forms the foundation for more complex probability scenarios.

Test your understanding of key concepts in Chapter 4 of ISDS. This quiz covers essential topics such as classical and subjective probability, with real-world examples for application. Perfect for reinforcing your knowledge before exams!