If S is the sample space of a random experiment, then P(S) = A) 1/4 B) 1/8 C) 0 D) 1
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Answer:
Before rolling a die you do not know the result. This is an example of a random experiment. In particular, a random experiment is a process by which we observe something uncertain. After the experiment, the result of the random experiment is known. An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set. Here are some examples of random experiments and their sample spaces:
Random experiment: toss a coin; sample space: S={heads,tails} or as we usually write it, {H,T}.
Random experiment: roll a die; sample space: S={1,2,3,4,5,6}.
Random experiment: observe the number of iPhones sold by an Apple store in Boston in 2015; sample space: S={0,1,2,3,⋯}.
Random experiment: observe the number of goals in a soccer match; sample space: S={0,1,2,3,⋯}.
When we repeat a random experiment several times, we call each one of them a trial. Thus, a trial is a particular performance of a random experiment. In the example of tossing a coin, each trial will result in either heads or tails. Note that the sample space is defined based on how you define your random experiment. For example,
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Answer:
If S is the sample space of a random experiment, then P(S) = D) 1