Should I memorise formulae or draw a table for IB probability?

Draw the sample space first. Two dice give only 36 ordered outcomes, and once the table is written the denominator appears by itself; formulae merely compress the table and invite double counting.

Does the expected value mean the outcome most likely to happen?

No. The expected value is a long-run average and need not be a possible outcome at all: a single die has expectation 3.5, which can never be rolled.

IB Mathematics: Probability and Expectation (Intermediate, 10 Questions)

2026-11-06

Tutor Prep Guide · IB Mathematics

Ten intermediate items on expectation and independence: computing E(X) from a distribution, using independence for intersections and unions, conditional probability, adjacent objects in permutations and binomial counting, each with a note.

Quick answer Answers in order: 2.1, 7, $15, 0.7, 9/25, 0.3, 1/3, 3.5, 5/16, 0.5. Multiply directly only when events are independent; otherwise use conditional probability.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 35 minutes
Difficulty mix	Intermediate 10
Chapter	Chapter: IB Mathematics: Probability and Expectation
Level	IB

02 Questions (10 items)

IntermediateA random variable X takes the values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3. Find E(X).
IntermediateTwo fair dice are rolled and S is the total. Find E(S).
IntermediateA game pays $50 with probability 0.2, $10 with probability 0.5 and nothing otherwise. Find the expected payout.
IntermediateA and B are independent with P(A) = 0.4 and P(B) = 0.5. Find P(A union B).
IntermediateA bag holds 3 red and 2 blue balls. A ball is drawn, replaced, then drawn again. Find the probability that both are red.
IntermediateGiven P(A and B) = 0.15 and P(B) = 0.5, find P(A given B).
IntermediateSix students line up at random. Find the probability that two named students stand next to each other.
IntermediateA fair die is rolled once. Find the expected score.
IntermediateA fair coin is tossed 5 times. Find the probability of exactly 2 heads.
IntermediateX takes only the values 3 and 7, and E(X) = 5. Find P(X = 7).

03 Answers and one-line notes

#	Answer	One-line note
1	2.1	E(X) = 1(0.2) + 2(0.5) + 3(0.3) = 0.2 + 1.0 + 0.9 = 2.1.
2	7	Each die has expectation 3.5, and expectation adds, so 3.5 + 3.5 = 7.
3	$15	50(0.2) + 10(0.5) + 0(0.3) = 10 + 5 = 15 dollars.
4	0.7	Independence gives P(A and B) = 0.4 x 0.5 = 0.2, so P(A union B) = 0.4 + 0.5 – 0.2 = 0.7.
5	9/25	Each draw is red with probability 3/5, so 3/5 x 3/5 = 9/25 = 0.36.
6	0.3	Use the conditional formula: P(A given B) = 0.15 / 0.5 = 0.3.
7	1/3	Treat the pair as one block: 2 x 5! = 240 arrangements out of 6! = 720, giving 1/3.
8	3.5	Sum the scores and divide by six: 21/6 = 3.5.
9	5/16	There are C(5,2) = 10 such sequences out of 32, giving 10/32 = 5/16.
10	0.5	With P(X = 7) = p: 3(1 – p) + 7p = 5, so 4p = 2 and p = 0.5.

04 What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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