Data Analysis and Probability in Geometry
Geometry EOC data questions usually pair with geometric contexts: conditional probability from two-way tables, expected counts, and geometric probability based on area. For a two-way frequency table, the probability of A given B is the count in the A-and-B cell divided by the total in row or column B, not divided by the grand total. That distinction is the single most common trap. Also be able to compute marginal frequencies (row and column totals) and to judge whether two categories appear independent by comparing conditional probabilities.
Geometric probability uses length, area, or volume ratios. If a point is chosen at random in a region, the probability it lands in a subregion equals the favorable measure divided by the total measure, assuming uniform randomness. For example, the probability of hitting a circular target inside a square is circle area divided by square area. Compound events: for independent events multiply probabilities; for mutually exclusive events add them; remember P(not A) = 1 - P(A).
Traps: using the grand total as the denominator for a conditional probability, forgetting to simplify ratios, mixing up "and" with "or," and using the wrong measure (comparing a length to an area).
Worked example. A square dartboard is 10 by 10, with an inscribed circle of radius 5. Probability of landing inside the circle = (25 pi) / 100 = pi / 4, about 0.785. Probability of landing outside the circle = 1 - pi/4, about 0.215.