Probability
Most SAT probability questions hide inside a two-way table. Adjust the counts below and watch how a conditional probability — restricting to just one row — changes as the numbers shift.
| Has a pet | No pet | Total | |
|---|---|---|---|
| Under 18 | 18 | 12 | 30 |
| 18 or older | 22 | 8 | 30 |
| Total | 40 | 20 | 60 |
Basic probability is favorable outcomes over total outcomes. A two-way table organizes counts across two categories at once, and gives you three different kinds of probability from the same data: a marginal probability uses a row or column total over the grand total; a joint probability uses one specific cell over the grand total; a conditional probability restricts you to just one row or column first, then asks about a cell within it — like “given that someone is under 18, what’s the probability they have a pet?”
For independent events (like separate coin flips or spins), multiply the individual probabilities together to find the probability that both happen. Complementary probabilities — an event and its opposite — always add up to 1.
A classic trap: counting students in two groups (like Spanish and French) and adding the totals directly. If some students are in both groups, that overlap gets double-counted unless you subtract it back out.