01 Key Concepts
Event (E)
Any subset of the sample space S. Example: rolling an even number, E = {2,4,6}.
Simple vs. Compound Events
A simple event has exactly one outcome (rolling a 3). A compound event has more than one (rolling an even number).
Complement of an Event
The complement of E (written E') contains every outcome in S that is NOT in E. P(E) + P(E') = 1.
Union of Events (A or B)
Contains every outcome that is in A, in B, or in both.
Intersection of Events (A and B)
Contains only the outcomes that are in both A and B at the same time.
Mutually Exclusive Events
Two events that cannot happen at the same time — their intersection is empty (rolling a 2 and rolling a 5 on one roll).
02 Key Formulas
- P(E) = n(E) / n(S)
- P(E') = 1 - P(E)
- P(A or B) = P(A) + P(B) - P(A and B)
03 Solved Examples
Example 1 A die is rolled. Let E = rolling an even number. Find P(E).
- E = {2,4,6}, so n(E) = 3.
- S = {1,2,3,4,5,6}, so n(S) = 6.
- P(E) = n(E)/n(S) = 3/6.
Answer: P(E) = 1/2
Example 2 Using the previous example, find P(E'), the probability of NOT rolling an even number.
- P(E') = 1 - P(E) = 1 - 1/2.
Answer: P(E') = 1/2
Example 3 A die is rolled. Let A = rolling an even number, B = rolling a number greater than 3. Find P(A or B).
- A = {2,4,6}, B = {4,5,6}. A and B (intersection) = {4,6}.
- P(A) = 3/6, P(B) = 3/6, P(A and B) = 2/6.
- P(A or B) = P(A) + P(B) - P(A and B) = 3/6 + 3/6 - 2/6.
Answer: P(A or B) = 4/6 = 2/3
04 Practice Questions
1A die is rolled. Let E = rolling a number less than 3. Find P(E).
2/6 = 1/3
2Find P(E') for the event above.
2/3
3Are 'rolling a 2' and 'rolling a 5' mutually exclusive on a single roll?
Yes
4A card is drawn from a deck. Let E = drawing a heart. Find P(E).
13/52 = 1/4
5If P(A)=0.3 and P(B)=0.4 and they're mutually exclusive, find P(A or B).
0.7
📄 Events — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.