Chapter 14: ProbabilityClass 11 Mathematics — summary, notes, extra questions & MCQ quiz

Summary

Building on random experiments and sample spaces, this chapter takes the axiomatic approach to probability. Any subset \(E\) of the sample space \(S\) is an event; \(\varphi\) is the impossible event and \(S\) the sure event. Events combine like sets: \(A\cup B\) is "A or B", \(A\cap B\) is "A and B", \(A'\) is "not A", and \(A-B\) is "A but not B". Two events are mutually exclusive if \(A\cap B=\varphi\), and a collection is exhaustive if its union is \(S\). Probability \(P\) assigns to each event a number satisfying \(P(E)\ge0\), \(P(S)=1\), and \(P(A\cup B)=P(A)+P(B)\) for mutually exclusive events, from which \(P(\varphi)=0\). For equally likely outcomes \(P(A)=\dfrac{n(A)}{n(S)}\). General results include the addition rule \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) and the complement rule \(P(\text{not }A)=1-P(A)\). These let us compute chances for coins, dice, cards and selections.

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