Probability · Quick Reference

Events Cheat Sheet

Probability · Lesson 2/8

In one line: an event is any subset of the sample space — a specific outcome or group of outcomes we're interested in tracking.

Key Ideas

1Event (E). Any subset of the sample space S. Example: rolling an even number, E = {2,4,6}.

2Simple vs. Compound Events. A simple event has exactly one outcome (rolling a 3). A compound event has more than one (rolling an even number).

3Complement of an Event. The complement of E (written E') contains every outcome in S that is NOT in E. P(E) + P(E') = 1.

4Union of Events (A or B). Contains every outcome that is in A, in B, or in both.

5Intersection of Events (A and B). Contains only the outcomes that are in both A and B at the same time.

A die is rolled. Let E = rolling an even number. Find P(E).

P(E) = 1/2

Using the previous example, find P(E'), the probability of NOT rolling an even number.

P(E') = 1/2

A die is rolled. Let A = rolling an even number, B = rolling a number greater than 3. Find P(A or B).

P(A or B) = 4/6 = 2/3

P(E) = n(E) / n(S)

P(E') = 1 - P(E)

P(A or B) = P(A) + P(B) - P(A and B)

A die is rolled. Let E = rolling a number less than 3. Find P(E).

2/6 = 1/3

Find P(E') for the event above.

2/3

Are 'rolling a 2' and 'rolling a 5' mutually exclusive on a single roll?

Yes