Two Examples

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).[br]What is the experiment?

All the ages of the students in your course. 0.59049 The probability that every student in your sample is over 18 years old. Survey 5 students and record their ages. Everyone in the course is over 18 years old. (19,30,24,20,27) ages At least one student is 18 or younger in the sample. All 5 students in the sample are over 18 years old. All the possible ages of 5 students chosen from the class. All the students in your course.

Pertinent event

What is the event we are checking?

All 5 students in the sample are over 18 years old. All the ages of the students in your course. Survey 5 students and record their ages. All the students in your course. At least one student is 18 or younger in the sample. Everyone in the course is over 18 years old. (19,30,24,20,27) ages The probability that every student in your sample is over 18 years old. All the possible ages of 5 students chosen from the class. 0.59049

What is an one possible outcome?

Survey 5 students and record their ages. All the students in your course. All 5 students in the sample are over 18 years old. Everyone in the course is over 18 years old. The probability that every student in your sample is over 18 years old. At least one student is 18 or younger in the sample. All the possible ages of 5 students chosen from the class. 0.59049 All the ages of the students in your course. (19,30,24,20,27) ages

What is the sample space?

At least one student is 18 or younger in the sample. All 5 students in the sample are over 18 years old. (19,30,24,20,27) ages All the students in your course. All the possible ages of 5 students chosen from the class. The probability that every student in your sample is over 18 years old. Everyone in the course is over 18 years old. All the ages of the students in your course. Survey 5 students and record their ages. 0.59049

Which could be the probability of the pertinent event?

At least one student is 18 or younger in the sample. Everyone in the course is over 18 years old. 0.59049 All the ages of the students in your course. (19,30,24,20,27) ages Survey 5 students and record their ages. All the possible ages of 5 students chosen from the class. All the students in your course. The probability that every student in your sample is over 18 years old. All 5 students in the sample are over 18 years old.

Definition. compliment

The compliment of an event is the absence of the event.[br]The compliment of event A[color=#ff0000][u] is all of the outcomes not in A.[/u][/color]

Notation. compliment

The compliment of an event A is denoted [math]A^C[/math] or sometimes as [math]\text{\overline{A}}[/math] 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?

The probability that every student in your sample is over 18 years old. All the possible ages of 5 students chosen from the class. Everyone in the course is over 18 years old. At least one student is 18 or younger in the sample. (19,30,24,20,27) ages All 5 students in the sample are over 18 years old. Survey 5 students and record their ages. All the ages of the students in your course. All the students in your course. 0.59049

Review. Choose 1 or more.

According to our previous chapters, what is the population?

All 5 students in the sample are over 18 years old. 0.59049 Survey 5 students and record their ages. (19,30,24,20,27) ages All the possible ages of 5 students chosen from the class. At least one student is 18 or younger in the sample. All the students in your course. Everyone in the course is over 18 years old. All the ages of the students in your course. The probability that every student in your sample is over 18 years old.

What is the sample size?

Choose all that apply

The survey should be done

repeatedly with a random sample without replacement with replacement

Multiple answer

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

E' [math]\text{\overline{E}}[/math] {E} not E [math]\text{\underline{E}}[/math] [math]E^C[/math] [math]\underscore E[/math]

Second Example. Now You Try.

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

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

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

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

How many outcomes are in each of these events?

Guess, P(W)=

Let event B be getting exactly two heads. (Note event B is composed of two outcomes.) What is the compliment of B?[br][math]B^C[/math] = __

What is another term for a 'simple event'?

An outcome An event A probability