Probability from a One-Way Data Display

Almost every probability question on this test reduces to one move: count how many outcomes fit what you want, count how many outcomes exist total, and divide. A one-way data display just organizes those counts into categories, so the question is really asking you to read a table correctly. There is no formula to memorize beyond part over whole.

Mechanically, take the frequency of the outcome you care about and divide by the sum of all frequencies in the display. That fraction always lands between 0 and 1, because the favorable count can never exceed the total, and it can never be negative. If you add more items to one category, like dropping extra red marbles into a jar, both numbers in the fraction can shift: the favorable count goes up, and so does the total, so the new probability needs both pieces rewritten, often as an expression with a variable rather than a single number.

This connects directly to conditional probability, which is the next step up: instead of dividing by the whole table, you divide by just one row or column of it, restricting the total to a smaller group. It also sets up the distinction between theoretical probability, a fixed property of a process, and relative frequency, what one real set of trials happened to produce. Expect questions that test whether you can tell the two apart, since a real run of data almost never matches the theoretical value exactly, especially with small samples.