What the board asks

We went through the ISC board papers, question by question, and matched each question to a topic. Here is what was asked, how often, and what was never asked.

Mathematics: 309 topics in the 2027 syllabus, across 11 units. The board has asked 255 of them at least once. 54 were never asked in the papers we checked.

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M11 Probability

All the topics in Mathematics: Probability

Asked topics first, the most asked at the top. Tap a topic to see what to write, the result, the years, and the real board questions.

30 topics shown

#	Topic	Type	Marks	Times asked	Last asked	Status
1	Mean (expected value) of a random variableAdd a column x P(x) to the distribution table, sum it, and state E(X) with a word on what it means in the story if asked.	Sum	2	6 papers	2026	Asked
2	Standard results: complement, addition theorem, mutually exclusive eventsWrite the law you use (complement, addition theorem, or P(A or B) = P(A) + P(B) for mutually exclusive events), substitute the given values and give the answer as a fraction in lowest terms or a decimal.	Statement	1	4 papers	Specimen 2027	Asked
3	Total probability: choose a source at random, then drawDefine the partition events E1, E2, (E3) and the event A, write P(Ei) and P(A\|Ei) from the story, and add the products P(Ei) P(A\|Ei).	Sum	3	3 papers	Specimen 2027	Asked
4	Conditional probability from given P(A), P(B), P(A n B)Write the definition, find P(A n B) if it is not given (from the union or from the other conditional), substitute and simplify each required value.	Sum	2	3 papers	2025 improvement	Asked
5	Product rule for independent trials: with replacement, oddsFind the probability for one trial (convert odds a:b in favour to a/(a+b)), state that trials are independent, and multiply the probabilities for all trials.	Sum	1	3 papers	2025	Asked
6	Bayes' theorem word problem: shares and success ratesTurn the shares (percent of employees, people assigned, transport used) into priors and the success or failure rates into likelihoods for the observed event, apply Bayes' theorem, and simplify.	Sum	5	3 papers	2025 improvement	Asked
7	Distribution of a count from draws without replacementState the values of X, find P(X = r) for each by combinations (or the multiplication theorem with all orders), write the table, check the sum is 1, and find the mean if asked.	Sum	3	3 papers	2025 improvement	Asked
8	At least one success among independent eventsWrite the probability of failure for each person or shot, multiply them for 'all fail', and subtract from 1.	Sum	1	3 papers	2024	Asked
9	Bayes' theorem word problem: bags, boxes, coins or dieName the events (which bag or box, and the observed draw), write the priors from how the bag is chosen, find the likelihoods (with combinations if two items are drawn), apply Bayes' theorem, and give the answer as a fraction in lowest terms.	Sum	5	3 papers	2024	Asked
10	Independent events: find union, neither, or unknown probabilityWrite P(A n B) = P(A) P(B) for independent events, substitute in the addition theorem or in P(A' n B') = P(A') P(B'), and solve for the value or the unknown.	Sum	2	3 papers	2023	Asked
11	Exactly k or at least k of three independent eventsWrite every case as a product (for exactly two: A B C' + A B' C + A' B C), evaluate each product, add, and for 'at least two' add the 'all three' case; for two people contradicting, add P(A true, B false) and P(A false, B true).	Sum	3	3 papers	2023	Asked
12	Find unknown constants in a distribution, then probabilitiesWrite the given conditions (sum = 1 and any given P(X <= a) or P(X >= b)) as equations, solve for the unknowns, and find the probability asked by adding the right entries.	Sum	1	2 papers	Specimen 2027	Asked
13	Multiplication theorem: successive dependent draws or eventsWrite the events in order, write P(first) and P(second \| first) from the changed situation, multiply, and add the products for each case when several orders give the event.	Sum	2	2 papers	2026	Asked
14	Transfer balls between bags, then drawList the possible transfers (both white, both black, one of each) with their probabilities, find the draw probability from the new second bag in each case, and add the products.	Sum	3	2 papers	2026	Asked
15	Random variable: possible values and a valid distributionList the values the random variable can take from the story, and check a table is a valid distribution by showing each P is between 0 and 1 and the P values add to 1.	Statement	1	2 papers	2026	Asked
16	Addition theorem word problem: two overlapping groupsDefine events A and B in words, write P(A), P(B) and P(A n B) from the counts, and use the addition theorem and complements for 'A or B', 'neither' and 'A but not B'.	Sum	2	2 papers	2025 improvement	Asked
17	Classical probability by selection using combinationsCount the total ways nCr of choosing the items, count the favourable ways as a product of combinations for each group (adding cases for 'all from the same' or 'at least one'), and divide.	Sum	2	2 papers	2025	Asked
18	Equally likely sequences: count patterns such as runsWrite the total number of equally likely sequences (for example 2^n), split the favourable sequences into non-overlapping cases by where the pattern starts, count each case, add, and divide.	Sum	2	1 paper	Specimen 2027	Asked
19	Read conditional probabilities from a story; complementsName the events, translate each sentence of the story into P(B\|A), P(B'\|A) or P(B\|A'), and use P(B'\|A) = 1 - P(B\|A) to get the value asked.	Sum	1	1 paper	Specimen 2027	Asked
20	Find P(A\|B) in symbols from P(A), P(B\|A), P(B\|A')Find P(A n B) and P(A' n B) by the multiplication theorem, add them for P(B) by total probability, divide, and simplify the algebraic fraction to match an option.	Sum	1	1 paper	Specimen 2027	Asked
21	Bayes with test accuracy: false positive or negativeWrite the prior for the rare condition, the test's hit rate and false alarm rate, find the probability of a positive result by total probability, then the posterior by Bayes' theorem, rounded as asked.	Sum	5	1 paper	Specimen 2027	Asked
22	Bayes with a host's choice: posteriors, then decideSet equal priors for where the prize is, write the probability of the host's action for each case, apply Bayes' theorem to get each posterior, and state and justify the better choice by comparing them.	Give reason	5	1 paper	Specimen 2027	Asked
23	Show that two events are or are not independentList the sample space, write A, B and A n B as sets, find P(A), P(B), P(A n B), compare P(A n B) with P(A) P(B), and state the conclusion.	Proof	2	1 paper	2026	Asked
24	Case study: two-day chain with total probability and BayesDraw a two-stage tree (today, tomorrow) with the given probabilities, use it for total probability, the complement, the reverse conditional by Bayes' theorem, and the probability of a whole path by the multiplication theorem.	Sum	5	1 paper	2026	Asked
25	Distribution from a frequency tableFind any missing frequency from the total, divide each frequency by the total to get P(X = x), write the table, verify the sum is 1, and find the mean if asked.	Sum	2	1 paper	2026	Asked
26	Assertion-reason on conditional, exclusive and independent eventsTest the assertion and the reason separately with the definitions (or a quick counter-example), decide whether the reason explains the assertion, and choose the option.	Give reason	1	1 paper	2025	Asked
27	Case study: distribution from listed outcomesComplete the table of outcomes, count those giving each value of X, write the distribution table, find a probability such as P(X < k), and find the expected value.	Sum	5	1 paper	2024	Asked
28	Variance and standard deviation of a random variableAdd columns x P(x) and x^2 P(x), find the mean, then Var(X) = sum of x^2 P(x) - (mean)^2, and SD as its square root.	Sum	2	1 paper	2018	Not in syllabus
29	Binomial probabilities for n repeated independent trialsState n, p and q, write P(X = r) = nCr p^r q^(n - r), and add the right terms for 'not more than', 'at least' or 'equal numbers', using the complement where it is shorter.	Sum	3	2 papers	2020	Not in syllabus
30	Binomial distribution from given mean and varianceWrite np = mean and npq = variance, divide to get q, then p and n, write the distribution P(X = r) = nCr p^r q^(n - r), and find the probability asked.	Sum	2	1 paper	2019	Not in syllabus

This list was made from the 2027 syllabus and checked with 10 board papers, including the 2027 specimen paper. It is not yet checked with the textbook.

The 10 topics Mathematics papers ask most

Counted on the board papers from 2018 to the 2027 specimen paper, which every unit has been checked against.

1.Formulate an LPP from a word problemM10 Linear Programming · asked 7 times since 2018
2.Scalar and vector projection of one vector on anotherM8 Vector Algebra · asked 6 times since 2018
3.Mean (expected value) of a random variableM11 Probability · asked 6 times since 2018
4.Find the inverse of an invertible algebraic function and verifyM1 Relations and Functions · asked 5 times since 2018
5.Principal value of expressions and nested inverse trigM1 Relations and Functions · asked 5 times since 2018
6.Evaluate or show zero without expanding, using propertiesM2 Algebra: Matrices and Determinants · asked 5 times since 2018
7.Prove a determinant equals a factorised expression using propertiesM2 Algebra: Matrices and Determinants · asked 5 times since 2018
8.Definite integral of a modulus functionM5 Calculus: Integrals · asked 5 times since 2018
9.Case study or linked parts on lines and planesM9 Three-Dimensional Geometry · asked 5 times since 2018
10.Equations solved with the complementary identitiesM1 Relations and Functions · asked 4 times since 2018

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