Math, Problem-Solving and Data Analysis, Stage 3
Probability on the SAT: lesson and practice
Probability = favorable outcomes ÷ total outcomes. In a two-way table, the key is the denominator: if the question says "if a person from group X is chosen", divide by group X’s total only. For independent events, "both" means multiply; "not" means subtract from 1.
Loading practice…
| Question wording | Denominator |
|---|---|
| "chosen at random from all…" | Grand total |
| "If a Grade 11 student is chosen…" | Grade 11 row total |
| "If a student who chose science is chosen…" | Science column total |
Cover every row or column that is not part of the "if" group before you calculate.
Common mistakes
Dividing by the grand totalConditional questions limit the group.
Adding for "both"Independent events multiply.
Forgetting the complementP(not A) = 1 − P(A).
Sample questions with answers
1. 6 red, 3 blue and 2 green marbles. P(blue)?
- 3/8
- 3/11 (correct)
- 1/3
- 8/11
3 out of all 11 marbles.
2. Morning shift: 30 walked, 24 used transport. If a morning worker is chosen, P(walked)?
- 30/91
- 5/9 (correct)
- 15/28
- 54/91
30 out of the 54 morning workers.
3. P(rain) = 2/5. P(no rain)?
- 2/5
- 3/5 (correct)
- 2/3
- 1/5
1 − 2/5 = 3/5.
Frequently asked questions
How many probability questions are on the SAT?
Probability is part of Problem-Solving and Data Analysis. Problem-Solving and Data Analysis makes up about 15% of SAT Math, roughly 5 to 7 questions.
What is conditional probability?
The probability of an event within a limited group, calculated using that group’s total as the denominator.
When do I multiply probabilities?
When both of two independent events must happen.