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SAT Math / Problem-Solving and Data Analysis

SAT topic

Probability

How often an outcome should occur in a well-defined set.

Learning goals

  • Write a probability as a favorable-count over a total-count.
  • Distinguish 'and' from 'or' when counting outcomes.

Explanation

A basic probability is a fraction: the number of outcomes you want, divided by the number of equally likely outcomes in the sample space. Read the sentence that defines the whole group first. If a table shows 40 students and 12 play a sport, the probability a randomly chosen student plays a sport is 12/40, not 12 by itself.

Compound events need extra care. 'And' usually narrows the count; 'or' usually widens it, and you must not double-count overlap. If the problem samples without replacement, the total shrinks after the first pick. Keep the units as a probability between 0 and 1 unless the question asks for a percent.

Common mistakes

  • Adding probabilities that are not mutually exclusive without subtracting the overlap.
  • Changing the sample space after a draw and forgetting to update the denominator.

Practice

1 of 2Percent problems · easy · multiple choice

A quantity increases from 50 to 65. What is the percent increase?

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Quick review

  1. 01Name the sample space in a short phrase.
  2. 02Count favorable outcomes after applying every condition.
  3. 03Reduce the fraction or convert to a percent only if asked.
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Related resources

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