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 (Foundation, 10 Questions)

2026-11-06

Tutor Prep Guide · IB Mathematics

Ten foundation items on classical probability: equally likely outcomes, complementary events, the two-dice sample space and expected counts. Each answer starts from favourable over total outcomes and is reduced to lowest terms, with a note.

Quick answer Answers in order: 1/2, 2/5, 1/4, 1/2, 1/3, 0.65, 1/6, 2/5, 0.93, 10 times. Every item is favourable outcomes over total outcomes, reduced to lowest terms.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 25 minutes
Difficulty mix	Foundation 10
Chapter	Chapter: IB Mathematics: Probability and Expectation
Level	IB

02 Questions (10 items)

FoundationA fair die is rolled once. What is the probability that the score is even?
FoundationA bag holds 4 red and 6 blue balls. One ball is drawn at random. What is the probability that it is red?
FoundationOne card is drawn at random from a standard pack of 52. What is the probability of a heart?
FoundationTwo fair coins are tossed together. What is the probability that both show the same face?
FoundationA fair die is rolled once. What is the probability of a score greater than 4?
FoundationThe probability of an event is 0.35. What is the probability of its complement?
FoundationTwo fair dice are rolled together. What is the probability that the total is 7?
FoundationOne letter is chosen at random from A, B, C, D and E. What is the probability that it is a vowel?
FoundationOf 100 items, 7 are faulty. One item is chosen at random. What is the probability that it is not faulty?
FoundationA fair die is rolled 60 times. How many sixes are expected?

03 Answers and one-line notes

#	Answer	One-line note
1	1/2	Three of the six outcomes (2, 4 and 6) are even, so 3/6 simplifies to 1/2.
2	2/5	There are 4 favourable outcomes out of 10, and 4/10 simplifies to 2/5.
3	1/4	There are 13 hearts in the pack, and 13/52 simplifies to 1/4.
4	1/2	Two of the four equally likely outcomes (HH and TT) are the same, so 2/4 = 1/2.
5	1/3	Only 5 and 6 qualify, so the probability is 2/6 = 1/3.
6	0.65	The complement is 1 minus the original probability: 1 – 0.35 = 0.65.
7	1/6	Six of the 36 ordered outcomes total 7, and 6/36 simplifies to 1/6.
8	2/5	Only A and E are vowels, so the probability is 2 out of 5.
9	0.93	The 93 sound items give 93/100 = 0.93.
10	10 times	The expected count is the number of trials times the probability: 60 x 1/6 = 10.

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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