CAIIB · Advanced Bank Management · Module A — Statistics
CAIIB ABM Unit 6 — Theory of Probability: Free MCQs with Explanations
By Swarnakshi Jha (ex-banker) · Updated 29 October 2026 · Paper I of the December 2026 cycle (Sunday 6 December 2026)
This is the free practice page for CAIIB ABM Unit 6 — Theory of Probability (Module A — Statistics). The CAIIB Mock Centre holds 179 questions on this unit alone, every one with a why-right / why-wrong explanation; below are the facts examiners keep returning to, five practice questions with explanations, and the traps that cost marks.
ABM · Module A179 MCQs in the Mock Centre5 free belowPaper on 6 December
Key facts examiners test from this unit
Counting, sample space and events — probability measures chance between 0 and 1; count outcomes with n!, ⁿPᵣ (order matters) and ⁿCᵣ (order does not), then classify events.
Classical probability and the addition theorem — P(A) = favourable ÷ total equally likely cases; for "A or B" add and subtract the overlap; use complements for "at least one".
Conditional probability and independence — P(A/B) = P(A ∩ B) ÷ P(B); multiply along a sequence; independent events multiply directly; unknown first draws use total probability.
5 free practice questions — tap an option
Five practice questions from this unit. Answers lock on the first tap, exactly as in the exam, and an explanation opens underneath. The Mock Centre has all 179 questions on this unit, from easy to tough, with caselets and key-in numericals, why every other option is wrong and the exam tip — and tracks your score and revision dates.
Question 1 of 5
A branch counts the number of cheques returned unpaid in a day. Which of these is an impossible event?
Why (d): The count of returned cheques can only be a whole number 0, 1, 2, …, so 2.5 is not in the sample space; an event with no outcomes is an impossible event, with probability 0. The other events are possible, however unlikely. (a) is wrong: No returns is a possible outcome, a count of 0. (b) is wrong: Three returns is a possible whole-number count. (c) is wrong: A busy day can see more than 10 returns; unlikely is not impossible.
Question 2 of 5
The conditional probability of A given that B has occurred is…
Why (b): Knowing that B has occurred shrinks the sample space to B, so P(A/B) is the share of B that is also A: P(A ∩ B) ÷ P(B), with P(B) > 0. (a) is wrong: Dividing by P(A) gives P(B/A), the reverse condition. (c) is wrong: The product gives P(A ∩ B) only for independent events. (d) is wrong: The union is not the overlap of A with B.
Question 3 of 5
Which condition is NOT required for a variable to follow a binomial distribution?
Why (a): The binomial needs n fixed, independent trials with two outcomes and a constant p; p can be any value between 0 and 1 (p = 0.5 only makes it symmetric). (b) is wrong: A fixed number of trials n is a required condition. (c) is wrong: Independence of trials is a required condition. (d) is wrong: A constant probability of success is a required condition.
Question 4 of 5
What are the mean and variance of the standard normal variable Z?
Why (c): The textbook defines Z as the normal variable with μ = 0 and σ² = 1; any normal X becomes Z through Z = (X − μ) ÷ σ. (a) is wrong: The variance of Z is 1. (b) is wrong: It swaps the two parameters. (d) is wrong: Μ and σ² are the parameters of X, before standardising.
Question 5 of 5
When an option is exercised, who must sell or buy the underlying asset?
Why (a): The holder has the right to exercise; the writer is the person on whom the right is exercised and must perform. (b) is wrong: The holder chooses whether to exercise and has no obligation. (c) is wrong: The textbook places the obligation on the writer. (d) is wrong: Mutual obligation is a feature of forwards, not options.
0 of 5 answered.
Traps in this unit
Using ⁿPᵣ for a committee.
Calling events exclusive when they can occur together.
Adding overlapping probabilities without subtracting P(A ∩ B).
Practise all 179 questions on Unit 6. The free CAIIB demo opens Units 1–2 of every paper with full explanations; the ABM Online Mock Centre unlocks all 4,600+ ABM questions, the full-length papers with caselets and key-ins, module mocks and Smart Revision for 18 months (₹1,499).
Independent study aid — not affiliated with, endorsed by, or sponsored by the Indian Institute of Banking & Finance (IIBF). Exam pattern, dates, fees and passing criteria are set by IIBF — always confirm the current rules at iibf.org.in. CAIIB content follows rules and developments up to IIBF's cut-off of 30 June 2026 (where a rule changed later, the update box says so); verify from official sources before relying on them in practice.