2. Unconditional, Conditional, and Joint Probabilities

d. distinguish between unconditional and conditional probabilities;

What does it mean to say “the complement of event A”? The complement is the event that A does not happen. A and A^c are mutually exclusive. \(A^c\)

What is unconditional probability (or marginal probability)? How is it denoted mathematically? It is simply the probability of an event happening. The event is not conditional on something else happening first. It is denoted by P(A)

What is a conditional probability? How is it denoted mathematically? It is the probability of an event happening when some other event has happened first. It is denoted by P(A | B)

What is a joint probability? How is it denoted mathematically? A joint probability is the probability of two events happening together. It is denoted as P(AB)

What is the joint probability of two mutually exclusive events happening? Zero. They can’t happen at the same time.

What is the multiplication rule for probabilities and when is it applicable? \(P(AB) = P(A|B) * P(B)\) - Used when we know the conditional probability of P(A|B) and want to know the joint probability of P(AB)

In a question, what would the words “given that” or “you are told that” signify in regards to probability? This language means that the probability is conditional