### Definitions

**Sample space** the list of all possible outcomes.

**Event** the outcomes that meet the requirement.

**Probability** for event A,

**Dependent events** two events are dependent if the outcome of event A affects the outcome of event B so that the probability is changed.

**Independent events** two events are independent if the fact that A occurs does not affect the probability of B occurring.

**Conditional probability** the probability of A, given that B has happened:

### 6.1. Single events

**Mutually exclusive**

P(A∪B) = P(A) + P(B)

P(A∩B) = 0

**Combined events**

P(A∩B) = P(A) + P(B) − P(A∪B)

A∪B (union)

A∩B (intersect)

If independent: P(A∩B) = P(A) × P(B).

**Compliment, A′** where P(A′) = 1 − P(A)

**Exhaustive** when everything in the sample space is contained in the events

### 6.2. Multiple events

Probabilities for successive events can be expressed through tree diagrams or a table of outcomes.

- one event and another, you multiply
- one event or another, you add

### 6.3. Distributions

For a distribution by function the domain of X must be defined as ∑P(X = x) = 1.

**Expected value** E(X) = ∑xP(X = x)

**Binomial distribution X ∼ B(n, p)** used in situations with only 2 possible outcomes and lots of trials

On calculator

- Binompdf(n,p,r) P(X = r)

- Binomcdf(n,p,r) P(x ≤ r)

Mean = np

Variance = npq

**Normal distribution X ∼ N(μ, σ ^{2})**

where μ = mean, σ = standard deviation

On calculator:

- normcdf(lowerbound, upperbound, = μ, σ)

- invnorm(area, = μ, σ)