167 questions · 29 question types identified
Questions that present a complete two-way table with all values given and ask for simple probabilities or conditional probabilities directly from the table using P(A∩B)/P(B) or similar.
A question is this type if and only if it provides conditional probabilities P(A|B) and asks to find joint probability P(A∩B) or marginal probabilities using the multiplication rule.
Questions where P(A|B) is found using Bayes' theorem with discrete events and a simple two-stage tree diagram (one initial choice, one outcome), typically involving 2-4 initial categories.
Questions where P(A), P(B), or P(A∩B) must first be calculated from given information (such as P(A∪B), Venn diagram data, or other relationships) before testing independence.
A random device (dice, spinner, etc.) is used to determine which population or group to sample from, requiring probability tree with initial branching based on device outcome.
A question is this type if and only if it involves drawing or using a tree diagram to represent sequential or two-stage events (e.g., mode of transport then arrival time, coin toss then marble selection).
Questions involving exactly two events (typically labeled with two letters like A and B, or W and L, or G and R) where students must find probabilities of unions, intersections, complements, or conditional probabilities using a two-circle Venn diagram.
Questions involving a diagnostic test with exactly two outcomes (positive/negative) and requiring calculation of probability of disease given test result using Bayes' theorem.
A question is this type if and only if it requires manipulating algebraic expressions involving probabilities (often with variables like x, p, q) to find relationships or specific values.
A question is this type if and only if it requires finding an unknown probability value (often denoted x, p, or m) by using the law of total probability or complement rule with given conditional probabilities.
Questions specifically asking for P(A|B') where B' is the complement of B (e.g., given NOT late, given does NOT have coffee, given does NOT have jam), requiring calculation of P(B') first.
Questions involving exactly three events (typically three sports, three methods, or three categories) where students must interpret or complete a three-circle Venn diagram to find probabilities or counts in various regions.
A question is this type if and only if it involves finding the probability of a prior event given a particular observed score or outcome (e.g., given score is 12, find probability spinner landed on even).
A question is this type if and only if it involves a game or match with multiple rounds where the probability of winning each round depends on previous outcomes.
Questions that provide partial information about a two-way table (some cells missing, or probabilities given instead of frequencies) and require completing the table before calculating probabilities.
A question is this type if and only if it involves selecting multiple items sequentially without replacement from a container with different colored or numbered objects.
A question is this type if and only if it requires constructing a complete probability distribution table for a random variable defined in a conditional probability context.
A question is this type if and only if it explicitly contrasts or involves scenarios where items are either replaced or not replaced between selections.
A question is this type if and only if it requires using complement rules, De Morgan's laws, or addition rules to find probabilities of unions, intersections, or complements.
A question is this type if and only if it involves three or more sequential stages or decisions where probabilities at each stage depend on previous outcomes.
Questions that provide P(A), P(B), and P(A∩B) directly and ask to test independence using the product rule P(A∩B) = P(A)×P(B).
Questions that provide P(A|B) or require calculating it, and test independence by checking if P(A|B) = P(A) or equivalent conditional probability relationships.
A single person or item is selected at random from the combined total of all populations, requiring weighted probabilities based on population sizes or proportions.
A question is this type if and only if it asks to determine whether events are mutually exclusive by checking if P(A∩B) = 0.
A question is this type if and only if it asks for the probability of exactly k occurrences of an event in n trials, requiring enumeration of specific sequences.
Questions involving conditional probability after selecting multiple items without replacement from containers (boxes, bags), where probabilities change after first selection.
Questions involving a diagnostic test with three outcomes (positive/doubtful/negative) requiring extended conditional probability calculations.
Questions involving a disease with multiple mutually exclusive types (e.g., type A and type B) where diagnostic characteristics differ by type.
A question is this type if and only if it asks for the probability of at least one occurrence of an event across multiple independent or dependent trials.