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| Random Experiment and Sample Space |
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| An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a 'deterministic' experiment. |
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| Example: |
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| While measuring the inner radius of an open tube, using slide callipers, we get the same result by performing repeatedly the same experiment. Many scientific and Engineering experiments are deterministic. |
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| If the outcome is one of the several possible outcomes, then such an experiment is called a "random experiment" or 'nondeterministic' experiment. |
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| In other words, any experiment whose outcome cannot be predicted in advance, but is one of the set of possible outcomes, is called a random experiment. |
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| If we think an experiment as being performed repeatedly, each repetition is called a trial. We observe an outcome for each trial. |
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| Example: |
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| An experiment consists of 'tossing a die and observing the number on the upper-most face' |
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| In such cases, we talk of chance of probability, which numerically measures the degree of chance of the occurrence of events. |
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| The set of all possible outcomes of a random experiment is called the sample space, associated with the random experiment. |
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| Note: |
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 Each element of S denotes a possible outcome. Each element of S is known as sample point. |
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 Any trial results in an outcome and corresponds to one and only one element of the set S. |
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| e.g., |
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| 1. In the experiment of tossing a coin, |
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| S = {H, T} |
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| 2. In the experiment of tossing two coins simultaneously, |
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| S = {HH, HT, TH, TT} |
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| 3. In the experiment of throwing a pair of dice, |
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| S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2),………. (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} |
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