Choose an exam and explore concepts through visual explanations, topic maps and revision checks. Open the full chapter notes whenever you need more detail.
THE VISUAL LEARNING STUDIO
See the idea. Understand the connection.
35 visual explanations across 29 chapters, with topic maps throughout the library.
The chapter index will grow as additional notes are prepared. Chapters shown here are a learning collection, not a claim that the entire exam syllabus is complete.
SEE IT. CONNECT IT. EXPLAIN IT.
Understand the chapter visually
Start with the topic map, then open each explanation below. Detailed concept diagrams are being added to this chapter.
Use Recall mode to hide explanations; tap or focus a card to reveal one. Expand any diagram for a larger view.
Study the expanded notes and the credited detailed textbook lessons. The current chapter index covers core topics; it is not a claim of exhaustive coverage of every examination syllabus. Check the official syllabus and primary references.
Probability — lesson overview
Events and outcomes
A sample space contains possible outcomes; an event is a set of outcomes. State the experiment before calculating.
For a finite set of equally likely outcomes, probability is favourable outcomes divided by total outcomes. Equal likelihood must be justified rather than assumed.
Probabilities lie between zero and one. The probability of the complement is 1−P(A).
Combining events
P(A∪B)=P(A)+P(B)−P(A∩B). Subtraction avoids counting the intersection twice.
Mutually exclusive events cannot occur together. Independent events satisfy P(A∩B)=P(A)P(B); exclusivity and independence are different properties.
For independent fair coin tosses, the probability of two heads is 1/2×1/2=1/4.
Conditional reasoning
Conditional probability P(A|B)=P(A∩B)/P(B) when P(B)>0. The condition restricts the comparison set.
P(A|B) need not equal P(B|A), because the conditioning populations and denominators differ.
Expected long-run proportions do not guarantee the exact pattern in a small sample, and independent past outcomes do not change the next fair toss’s probability.
When selecting without replacement, the composition of the remaining group changes, so successive draws need not be independent.
