Week 3 Probability Flashcards
A, B, C
What is the difference between subjective, frequency-based, and model-based probability?
Subjective Probability: Based on personal belief or observation.
Frequency-Based Probability: Derived from the proportion of occurrences over repeated trials.
Model-Based Probability: Based on mathematical models or known conditions.
How is the probability of an event (A) and its complement (A’) related?
P(A′) = 1−P(A) and 𝑃(𝐴) = 1−𝑃(𝐴′)
Define conditional probability and its notation.
The probability of one event occurring given another event has occurred. Notation: 𝑃(𝐴∣𝐵) read as “Probability of A given B.”
What is the relationship between
𝑃(𝐴∣𝐵) and 𝑃(𝐴and 𝐵)?
P(A∣B) = P(Aand B) / P(B)
P(AandB) = P(A∣B)*P(B)
What is the difference between independent and mutually exclusive events?
Independent Events: The occurrence of one event does not affect the probability of the other P(A∣B)=P(A).
Mutually Exclusive Events: Events cannot occur together P(AandB)=0.
What is Bayes’ Theorem?
P(A∣B)= P(B∣A)⋅P(A) / P(B), where 𝑃(𝐵) is the total probability of event 𝐵.
What is the formula for 𝑃(𝐴or 𝐵) in general?
P(AorB) = P(A) + P(B) − P(AandB)
What are the properties of probability for a single event?
0 ≤ P(A )≤ 1
𝑃(𝐴) = 0 if the event cannot occur.
𝑃(𝐴) = 1 if the event always occurs.
What is the probability of at least one event occurring when two events (A, B) are mutually exclusive?
P(AorB) = P(A) + P(B)
What is a joint probability, and how is it notated?
The probability of two events occurring together. Notation: 𝑃(𝐴and𝐵)
When are two events always mutually exclusive?
When 𝑃(𝐴and 𝐵) = 0
What does 𝑃(𝐴or 𝐴′) equal, and why?
1, because an event and its complement together cover all possible outcomes.
How are independent events different from mutually exclusive events?
Independent events can occur together, while mutually exclusive events cannot.
Give an example of subjective probability.
Based on my examination, I believe there’s a 70% chance the injury won’t require surgery.
Provide the formula for calculating conditional probability in the case of independence.
P(AandB) = P(A)*P(B)
Explain why
𝑃(𝐴∣𝐵) ≠ 𝑃(𝐵∣𝐴) in general.
Because 𝑃(𝐴∣𝐵) depends on the probability of 𝐵 and vice versa, and they can have different denominators.
