Probability
What this domain tests
Probability questions cover basic probability, complementary events, independent vs. dependent events, and counting. Most misses come from misidentifying whether events are independent and whether order matters.
Core concepts
- Probability = favorable outcomes ÷ total equally likely outcomes; always between 0 and 1.
- Complement: P(not A) = 1 − P(A). Often the fastest route.
- Independent events: P(A and B) = P(A) × P(B).
- Dependent events (no replacement): the denominator shrinks and the numerator may too.
- "Or" with overlap: P(A or B) = P(A) + P(B) − P(A and B).
- Expected value = sum of (value × probability).
Traps
- Using the original total after removing an item (replacement error).
- Adding probabilities for "and" or multiplying for "or."
- Double-counting outcomes in an "or" question.
- Forgetting that probabilities must sum to 1 across all outcomes.
Worked example
A bag has 5 red and 3 blue marbles (8 total). Draw two without replacement. P(both red) = (5/8) × (4/7) = 20/56 = 5/14. Note the second draw uses 7 marbles and 4 reds-that is the dependent adjustment. If the first marble were replaced, it would be (5/8) × (5/8) = 25/64. Comparing the two shows why "with replacement" must be stated and honored.
Rule of thumb
Ask two questions before computing: Are the events independent? and Does order matter? Then choose multiplication, addition, or a counting formula accordingly.
Data Interpretation
What this domain tests
Data Interpretation gives you tables, charts, or short passages and asks you to extract, compare, and compute. The math is usually simple; the challenge is reading carefully and choosing the right operation.
Core concepts
- Reading scales: check axis increments, units, and whether a bar chart starts at zero. A truncated axis exaggerates differences.
- Percent of total vs. percentage points: a change from 40% to 50% is 10 percentage points but a 25% relative increase.
- Rates from tables: per-capita or per-unit values require dividing one column by another.
- Trend vs. fluctuation: a one-period dip is not necessarily a trend.
- Rounding: match the precision the question asks for; do not over-round mid-calculation.
Traps
- Comparing raw counts when the question asks for rates (different group sizes).
- Mixing percentage points with percent change.
- Reading the wrong row, column, or year under time pressure.
- Assuming a chart's visual height equals a numeric ratio when the axis is broken.
Worked example
Two stores report sales. Store A: 300 of 1,200 customers bought (25%). Store B: 200 of 500 bought (40%). Store B has fewer buyers in raw count but a higher purchase rate. If the question asks which store "converted better," the answer is B at 40%. Always convert to a common base before comparing groups of different sizes.
Rule of thumb
Before computing, restate the question in your own words and label the exact column or category you need. Most errors here are selection errors, not arithmetic errors.