Probability for single events can be visually expressed through Venn diagram

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

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

**Probability** for event A,

Here the shaded circle.

Note: These events are also exhaustive as there is nothing outside of the events (nothing in the sample space).

**Mutually exclusive**

Example: What is the probability of picking each fruit?

Events do not overlap

P(A∪B) = P(A) + P(B)

P(A∩B) = 0

**Combined events**

Example: Of the apples 2 are red, 2 are green and 2 are yellow. What is the probability of picking a yellow apple?

The intersect is the area the events overlap.

P(A∩B) = P(A) + P(B) − P(A∪B)

Example: What is the probability of picking an apple or a yellow fruit?

The union is the area contain by both events.

P(A∪B) = P(A) + P(B) − P(A∩B)

When an event is exhaustive the probability of the union is 1.

A: apples

B: yellow fruit

Event is exhaustive so probability of union is 1.

**Compliment**

Example: What is the probability of not picking a yellow fruit?

Everything that is not in the stated event.

P(A′) = 1 − P(A)

A: apples

B: yellow fruit

P(B′) = 1 − P(B) = 1 − 0.6 = 0.4

**Conditional**

Example: What is the probability of picking an apple given I pick a yellow fruit?

The probability given that some condition is already in place.