HSC · Mathematics Standard 1 · Statistics · also VCE Probability & Everyday Maths live from the app

Basic probability calculations

When every outcome in a situation is equally likely, each single outcome has probability 1/n, where n is the total number of outcomes. The probability of an event A is then counted, not chosen: P(A) = number of favourable outcomes ÷ total number of outcomes. Because the favourable outcomes are some of the total, the answer always sits between 0 (nothing favourable) and 1 (everything favourable), and the outcomes outside A fill the rest, so P(not A) = 1 − P(A). This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.

mathematics standard 1 · statistics · basic probability calculationsdrag it · it is yours
the one idea

why this one carries the topic.

A scatterplot shows you two things moving together, and correlation puts a number on how tightly. But together isn't because — the line you draw predicts, it doesn't explain. Every question here is really asking: how strong is the pattern, and how far can you trust it?

A row of n equal outcome cells with k of them lit as the event A, above a 0-to-1 line split into P(A) and P(not A); the overlay reads P(A) = k/n as a fraction and a decimal, and the two colours always fill the whole line.

what examiners catch — Students write the ratio with the wrong denominator (favourable over not favourable, which is odds) or apply it when the outcomes are not equally likely. The mark comes from naming the sample space, counting both the favourable and the total outcomes, and giving the fraction in simplest form.
what you leave with

five things, not forty.

what's underneath

nothing here is a standalone fact.

knowhere maps every concept to what it rests on and what rests on it — 2 underneath this one, 4 built on top. Each one says why, in a sentence, not as an arrow on a diagram.

this conceptbasic probability calculationsA row of n equal outcome cells with k of them lit as the event A, above a 0-to-1 line split into P(A) and P(not A); the overlay reads P(A) = k/n as a fraction and a decimal, and the two colours always fill the whole line.
sits under itthe language of chancebecause the 0-to-1 scale is what the calculation has to land on
sits under itfractions, decimals and the number linebecause P(A) is read as a fraction and placed as a decimal on a 0-to-1 line.
built on itworking out probabilitiesbecause Favourable ÷ total is the starting rule the square is built from.
built on itconditional probability and independencebecause P(A) = n(A) ÷ n(S) for equally likely outcomes is what conditional probability restricts to B.
built on itrelative frequency and long-run probabilitybecause The theoretical probability the line settles on comes from counting equally likely outcomes.
built on itsampling methods comparedbecause A fair method means every member has an equal chance of selection, which is a probability idea.
the rest of statistics

4 more, same treatment.

Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.

correlation and causationlive →correlation and scatterplotsin the appcompound probability and tree diagramsin the appthe language of chancein the app
this is one of 865

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