Probability

Flashcards covering the fundamental concepts, rules, and formulas of probability as discussed in the lecture notes.

Probability

A value ranging from $0.00$ (totally unlikely) to $1.00$ (certain).

p(event A)

The probability that an event occurs, calculated as $\frac{A}{A+B}$ if an event can occur in $A$ ways and fail in $B$ ways.

Mutually exclusive

A condition where the occurrence of one event precludes the occurrence of another event, meaning they cannot happen together.

Independent events

Events where the occurrence of one has no effect on the probability of the occurrence of another event.

Additive rule

For mutually exclusive events, the probability of one event or another occurring is the sum of their separate probabilities, expressed as $p(A \text{ or } B) = p(A) + p(B)$.

Multiplicative rule

The probability of the joint occurrence of two or more independent events, calculated as the product of their individual probabilities: $p(A \text{ and } B) = p(A) \times p(B)$.

Additive rule (non-mutually exclusive)

A formula used when events can occur simultaneously, requiring the subtraction of the joint probability: $p(A \text{ or } B) = p(A) + p(B) - p(A \text{ and } B)$.

Conditional probability

The probability of one event given the occurrence of another, denoted as $p(B|A)$.

Multiplicative rule (non-independent events)

The formula used to find the joint occurrence of dependent events: $p(A \text{ and } B) = p(A) \times p(B|A)$.

Combinations

The number of ways to arrange a subset of objects, calculated using the formula $\frac{N!}{r!(N-r)!}$, where $N$ is the number of events and $r$ is the number of successes.

Exclamation marks (!)

In mathematics, this signifies to multiply the number by all smaller integers, also known as a factorial.

Binomial distribution formula

A formula that calculates combinations and probability for any one combination of getting $r$ successes out of $N$ trials, where $p$ is the probability of success on any one trial.

Normal distribution

The distribution that the binomial distribution is equal to when the number of events ($N$) is large.