Math ↠ Tree Diagram ↠ Multi-step experiments

Multi-step experiments

In contrast to single-step experiments, multi-step experiments have several individual trials.

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Repetition

Multi-step experiments consist of multiple trials carried out in succession.

Examples

Examples for multiple-step experiments are:

  • Throwing a dice several times in a row
  • Drawing 5 tickets from a lottery wheel

Outcome and sample space

An outcome in multi-step experiments also consists of several steps.
The sample space $\Omega$ can also be set up here.

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Repetition

The sample space $\Omega$ is the set of all possible outcomes of an experiment.

Example

A coin is flipped three times.
$H$ - head and $T$ - tail

  • Results

    Possible results would be: $(HHT)$ or $(THH)$

    Since it is a 3-step experiment, a single outcome is obtained from 3 different partial outcomes of the individual steps.

  • Sample space

    $Ω=\{HHH,$ $HHT,$ $HTH,$ $HTT,$ $TTT,$ $TTH,$ $THT,$ $THH\}$

    All outcomes together form the sample space. After throwing the coin three times, the outcome must be included in the sample space.