8.1: Conditional and Joint Probabilities Flashcards
Define random variable.
Random variable is an uncertain quantity/number.
Define outcome.
Outcome is an observed value of a random variable.
Define event.
Event is a single outcome or a set of outcomes.
Define mutually exclusive events.
Mutually exclusive events are events that cannot both happen at the same time.
Define exhaustive events.
Exhaustive events are those that include all possible outcomes.
What are the two defining properties of probability?
- The probability of any event is between 0 and 1.
- If a set of events is mutually exclusive and exhaustive, the probabilities of those events sum to 1. When probability of event = 1, the event is set to occur and the outcome is not random.
Give an example of a mutually exclusive and exhaustive event with a probability = 1.
Set of events (rolling die equal to 1, 2, 3, 4, 5, 6) is exhaustive and individual events are mutually exclusive so the probability = 1.
Certain that one of the values in this set of events will occur.
What is a subjective probability?
Subjective probability is the least formal method of developing probabilities and involves the use of personal judgement.
What are the two objective probabilities? Define both.
- Empirical probability is established by analyzing past data.
- Priori probability is determined using a formal reasoning and inspection process.
What is unconditional probability?
Unconditional probability refers to the probability of an event regardless of the past or future occurrence of other events.
What is conditional probability? What are the two key words used to define conditional probability?
Conditional probability is one where the occurrence of one event affects the probability of the occurrence of another event.
Key words are “given” and “likelihood”.
What is the addition rule of probability and how is it calculated? How is it different for mutually exclusive event vs. not mutually exclusive events?
Addition rule of probability is used to determine the probability that at least one of two events will occur.
P(A or B) = P(A) + P(B) - P(AB)
This equation is if the events A and B are not mutually exclusive; double counting must be avoided by subtracting the joint probability.
For mutually exclusive events, where the joint probability is zero, and the equation is the sum of the unconditional probabilities for each event.
P(A or B) = P(A) + P(B)
What is the total probability rule?
Total probability rule is used to determine the unconditional probability of an event, given conditional probabilities of mutually exclusive and exhaustive events.
The equation for total probability rule is the sum of joint probabilities.
What is the multiplication rule of probability and how is it calculated? How is it related to joint probability and how is it calculated?
Multiplication rule of probability is used to determine the joint probability of two events.
P(AB) = P(A|B) x P(B)
Joint probability of two events is the probability that they will both occur.
The joint probability of A and B is equal to the conditional probability that A will occur given B occurs times the unconditional probability of B.
