Mastering Probability Questions on the SAT

Probability questions on the SAT require a solid understanding of basic probability concepts and how to apply them to real-world scenarios.

On the Digital SAT exam, probability questions ask you to determine how likely a particular event is to occur. With 2 math modules and 44 questions total, there is a very good chance at least one probability question will show up (usually one or two per exam).

Step 1: Understand the Basics of Probability

Probability is the measure of how likely an event is to occur. It is expressed as a fraction: number of desired outcomes divided by total possible outcomes. For example, the probability of tails on a coin flip is 1/2.

Simple Probability

Finding the probability of a single event. Example: 5 red and 5 blue marbles. P(red) = 5/10 = 1/2.

Compound Probability

Two or more events together. Example: Two red marbles in a row without replacement: (5/10) x (4/9) = 2/9.

Either/Or Probability

One event or another. Example: P(ace or queen) = 4/52 + 4/52 = 8/52 = 2/13.

Conditional Probability

Probability given a condition. Example: 52 dancers, 14 are ballet. P(ballet | dancer) = 14/52 = 7/26.

Step 2: Identify the Type of Probability Question

Simple: Look for questions about a single event. Compound: Multiple events together. Either/Or: One event or another. Conditional: Look for "given" or "assuming."

Step 3: Apply the Appropriate Formula

Simple Probability Formula

P(E) = Number of favorable outcomes / Total possible outcomes

Example: P(rolling a 4) = 1/6. P(red marble from 5 red, 3 green, 2 blue) = 5/10 = 1/2.

Compound Probability Formula

Independent events: P(A and B) = P(A) x P(B). Dependent events: P(A and B) = P(A) x P(B|A).

Independent example: P(rolling 4 and flipping heads) = 1/6 x 1/2 = 1/12.
Dependent example: P(two aces without replacement) = 4/52 x 3/51 = 1/221.

Either/Or Probability Formula

Mutually exclusive: P(A or B) = P(A) + P(B). Non-mutually exclusive: P(A or B) = P(A) + P(B) - P(A and B).

Mutually exclusive: P(ace or king) = 4/52 + 4/52 = 2/13.
Non-mutually exclusive: P(heart or face card) = 13/52 + 12/52 - 3/52 = 22/52 = 11/26.

Conditional Probability Formula

P(B|A) = P(A and B) / P(A). Focus on the subset meeting the condition.

Example: 100 performers, 52 dancers, 14 ballet. P(ballet|dancer) = (14/100)/(52/100) = 14/52 = 7/26.

Step 4: Verify Your Answer

Check your work to ensure your answer makes sense. Re-read the question and confirm the correct type and formula were used.

Complete Example: Students recalling dreams: Group Y has 11 (1-4 dreams) + 68 (5+ dreams) = 79. Total recalling dreams: 164. P(Group Y) = 79/164.
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Frequently Asked Questions

The SAT tests simple probability, compound probability, either/or probability, and conditional probability.

Focus on the subset meeting the condition. Use P(B|A) = P(A and B) / P(A). For 52 dancers with 14 ballet, P(ballet|dancer) = 14/52.

Independent events do not affect each other (coin flips). Dependent events do (drawing without replacement). For independent, multiply directly. For dependent, adjust the second probability.