Probability and Likelihood
What is Probability?
Probability measures how likely an event is to occur. It is a number between 0 and 1 (inclusive) that quantifies uncertainty. On the SAT, probability questions appear frequently — mastering this topic can earn you several easy points.
The Fundamental Formula
$$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
- $P(A) = 0$ means the event is impossible
- $P(A) = 1$ means the event is certain
- $0 \le P(A) \le 1$ always
Probability Scale
Interactive visualization — available in the full lesson
2. Complementary Events
$$P(\text{not } A) = 1 - P(A)$$
The complement of event $A$ includes all outcomes NOT in $A$.
Example: If the probability of rain is $0.3$, then the probability of no rain is $1 - 0.3 = 0.7$.
Verification rule: Always check that $P(A) + P(\text{not } A) = 1$.