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%.
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
- Basic probability = favorable รท total
- For conditional probability ("given that"), change the denominator to the given group
- Two-way tables are the most common format on the SAT
- Use the complement () for "at least one" problems
- Independent events: multiply probabilities
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