Probability
Probability for IB Analysis and Approaches HL: counting, events, conditional probability, independence, tree diagrams and Bayes' theorem, with exam questions.
Probability measures how confident we can be that something uncertain will happen, with a number between and . In this topic you learn to count cases with combinatorics, to describe events with sets and Venn diagrams, to apply the properties of probability and to calculate when prior information changes the result: conditional probability, independence, tree diagrams, total probability and Bayes' theorem. In the IB exam this is the topic that appears most in both papers, almost always with a Venn diagram, a table or a tree; the key is to translate the question into one of those representations.
Recommended order
Follow the sections in order: combinatorics, events and set operations, probability and its properties, conditional probability and independence and total probability, Bayes' theorem and tree diagrams. At the end you have the IB exam questions grouped by type.
Basic set operations, fractions and percentages; topic 12 (descriptive statistics) helps but is not essential.
Sections in this topic
Combinatorics and the fundamental counting principle
Counting principle, permutations, arrangements and combinations: when order matters, repetition and nCr. IB Analysis and Approaches HL.
3 worked examples Section 2Random experiments, events and set operations
Sample space, events, union, intersection, complement, mutually exclusive events, De Morgan's laws and Venn diagrams. IB Analysis and Approaches HL.
3 worked examples Section 3Probability and its properties: Laplace, complement and union
Relative frequency, Laplace's rule, probability axioms, complement and union rules, with Venn diagrams and tables. IB Analysis and Approaches HL.
3 worked examples Section 4Conditional probability and independence of events
How to calculate P(A|B), apply the product rule, check whether two events are independent and read contingency tables. IB Analysis and Approaches HL.
3 worked examples Section 5Total probability, Bayes' theorem and tree diagrams
Tree diagrams with and without replacement, total probability and Bayes' theorem, reading the tree step by step. IB Analysis and Approaches HL.
3 worked examples End of topicIB exam questions: topic 14
IB exam questions on probability: counting, Venn diagrams, tables, conditional probability, tree diagrams and Bayes' theorem, with step-by-step solutions.
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