Probability
Class 11 Mathematics · Chapter 14
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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.
Events and types of eventsAlgebra of eventsMutually exclusive and exhaustive eventsAxiomatic approach to probabilityProbability of equally likely outcomesAddition and complement rules
Key terms
Event
Any subset \(E\) of the sample space \(S\).
Impossible and sure events
\(\varphi\) is impossible; \(S\) is the sure event.
Mutually exclusive events
Events with \(A\cap B=\varphi\) that cannot occur together.
Exhaustive events
Events whose union is the whole sample space \(S\).
Equally likely outcomes
Outcomes with the same probability, so \(P(A)=\dfrac{n(A)}{n(S)}\).
Addition rule
\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
Extra questions & answers
Try one from this chapter
An event in probability is: