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Two Examples

Author:DavidK

Surveys (Random Sampling)

Surveys are an example of a statistical experiment. The method for choosing a random sample can be repeated even if the exact results do not occur again. A random sample often requires making a list of the population and having a computer randomly choose the sample. This list is one way we create a "controlled" environment.

First example of an experiment

You take a survey of 5 students in your course. You are finding the probability that all 5 would be over 18 years old. Your survey result is ages (19,30,24,20,27). What is the experiment?

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Pertinent event

What is the event we are checking?

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What is an one possible outcome?

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What is the sample space?

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Which could be the probability of the pertinent event?

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Definition. compliment

The compliment of an event is the absence of the event. The compliment of event A is all of the outcomes not in A.

Notation. compliment

The compliment of an event A is denoted or sometimes as or A', and is read “not A” or “the compliment of A”.

Event E is that all 5 students sampled are over 18 years old. What is the compliment of E?

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Review. Choose 1 or more.

According to our previous chapters, what is the population?

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What is the sample size?

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The survey should be done

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Multiple answer

Which of the following stand for the compliment of event E?

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Second Example. Now You Try.

You flip one fair coin twice. You win a prize if you get at least one tail. What is the experiment?

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What event are we looking for? (i.e. in the context of a game, what event is a win?) Recall an event is one or more results (outcomes) of an experiment.

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Labeling the successful event W we can use set notation to show all the outcomes inside it. W = { ?? }

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What event is not a success? I.e. what counts as a loss or failure?

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How many outcomes are in each of these events?

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Guess, P(W)=

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Let event B be getting exactly two heads. (Note event B is composed of two outcomes.) What is the compliment of B? = __

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What is another term for a 'simple event'?

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