Counting principle and probability notes

This section is the Grade 11 language of probability that Grade 12 Paper 1 still assumes. You name an experiment, list a sample space $S$, pick an event $A$, and compute $P(A)=\dfrac{n(A)}{n(S)}$ when the outcomes…

This section sets theoretical probability against relative frequency. Theoretical probability is the fraction you write before you run the experiment, when the outcomes are equally likely…

This section is the Venn-diagram tool for two overlapping events. A rectangle is the sample space $S$. Circles inside that rectangle are events. The four regions of a two-set Venn are **only $A$**, the…

This section is mutually exclusive events. Two events are mutually exclusive if they cannot happen at the same time. Their intersection is empty: $A\cap B=\emptyset$. On a Venn they are two circles…

This section is complementary events. The complement of event $A$ is every outcome in the sample space $S$ that is not in $A$. Write it $A'$ (or $A^{c}$, or not $A$). Complementary events are mutually exclusive…

This section is events which are not mutually exclusive. Two events can happen together: they share outcomes, so $A\cap B\neq\emptyset$ and $P(A\text{ and }B)>0$. On a Venn the two circles overlap in a lens. Then…

This section is the symbol and set language the paper will print. AND is intersection $\cap$. OR is union $\cup$. NOT is the complement $'$. Learn both the symbol and the English word. Counts use $n(\cdot)$…

This section is the tree-diagram method for two-stage experiments. Draw first-stage branches, then second-stage branches from each of those ends. Label every branch with its outcome and its…

This section is the contingency table: a two-way frequency table. One classification runs down the rows, the other across the columns. Fill every inner cell, then the row totals, the column totals…

This section is the fundamental counting principle: count how many outcomes a sequence of choices produces. If stage 1 has $m$ options and stage 2 has $n$, there are $m\times n$ outcomes. The same product…

This section is counting inside a probability. When every arrangement is equally likely and the sample space is too large to list, $P(A)=\dfrac{n(A)}{n(S)}=\dfrac{n(\text{favourable arrangements})}{n(\text{possible arrangements})}$…