Probability questions on the SAT are based on counting and ratios โ€” no complicated formulas needed. Most questions involve tables, and the key is reading them carefully.

Basic Probability

Probability always falls between 0 and 1 (or 0% and 100%).

Example 1: A bag has 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?

Complementary Probability

Example 2: If there's a 30% chance of rain, the probability of no rain is or 70%.

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Two-Way Tables (Conditional Probability)

This is the #1 way the SAT tests probability. You'll see a table like this:

Right-handed Left-handed Total
Male 38 12 50
Female 42 8 50
Total 80 20 100

Example 3: What is the probability that a randomly selected student is left-handed?

Example 4: Given that a student is male, what is the probability that he is left-handed?

This is conditional probability โ€” we restrict to males only:

Notice the denominator changed to 50 (total males), not 100.

Example 5: What is the probability that a left-handed student is female?

"At Least One" Problems

For "at least one" questions, use the complement:

Example 6: A coin is flipped 3 times. What is the probability of getting at least one head?

Independent Events

Two events are independent if one doesn't affect the other.

Example 7: The probability of rain on Saturday is 0.3 and on Sunday is 0.4 (independent). What's the probability of rain on both days?

Practice Problems

Problem 1: A survey of 200 people found that 120 prefer coffee and 80 prefer tea. What is the probability a random person prefers tea?

Solution

Problem 2: Using the handedness table above, what is the probability that a randomly chosen female is right-handed?

Solution

Problem 3: A die is rolled twice. What is the probability of getting a 6 both times?

Solution

Key Takeaways

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