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Probability – Experiments, events and outcomes

📘 Notes

Experiments, Events and Outcomes

Probability describes how likely an event is to happen.

1. Key Definitions

  • An experiment is a process with an uncertain result.
  • An outcome is a possible result of an experiment.
  • An event is a set of one or more outcomes.

Probabilities are assigned on a scale from \(0\) to \(1\):

  • \(0\) means impossible
  • \(1\) means certain

If one object is chosen at random from \(n\) objects, then:

\[ P(\text{selecting any particular object})=\frac{1}{n} \]

If outcomes are equally likely, then:

\[ P(\text{event})=\frac{\text{number of favourable equally likely outcomes}}{\text{total number of equally likely outcomes}} \]

2. Useful Facts

The complement of \(A\) is written as \(A'\) or \(A^c\).

\[ P(A)+P(A')=1 \]

In \(n\) trials, event \(A\) is expected to occur:

\[ n\times P(A) \]

Notation:

  • \(A\cup B\) means “\(A\) or \(B\)”
  • \(A\cap B\) means “\(A\) and \(B\)”