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Chapter 4: Problem 1

Define the following terms: experiment, outcome, sample space, simple event, and compound event.

Short Answer

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An 'experiment' is a procedure or action with an uncertain outcome. An 'outcome' is a possible result of an experiment. 'Sample space' is the set of all possible outcomes of an experiment. A 'simple event' involves only one outcome. A 'compound event' involves two or more outcomes.

Step by step solution

01

Defining Experiment

In the field of probability theory and statistics, an 'experiment' refers to any procedure or action with an uncertain outcome where we can observe some random process, such as flipping a coin or rolling a die.
02

Defining Outcome

An 'outcome' refers to a possible result from an experiment. For instance, if flipping a coin is the experiment, the possible outcomes can be 'heads' or 'tails'.
03

Defining Sample Space

The 'sample space' of an experiment is the set of all possible outcomes. In the coin flipping experiment, the sample space would be {Heads, Tails}.
04

Defining Simple Event

A 'simple event' is an event in which only one outcome is observed from the sample space. In a coin flip, observing 'heads' can be an example of a simple event.
05

Defining Compound Event

A 'compound event' involves the combination of two or more simple events. For example, in rolling a die, an event that the outcome will be an odd number (1, 3 or 5) is a compound event as it includes multiple simple outcomes.

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Most popular questions from this chapter

The probability of a student getting an A grade in an economics class is \(.24\) and that of getting a B grade is \(.28\). What is the probability that a randomly selected student from this class will get an \(\mathrm{A}\) or a \(\mathrm{B}\) in this class? Explain why this probability is not equal to \(1.0\)

Many states have a lottery game, usually called a Pick-4, in which you pick a four-digit number such as 7359 . During the lottery drawing, there are four bins, each containing balls numbered 0 through 9\. One ball is drawn from each bin to form the four-digit winning number. a. You purchase one ticket with one four-digit number. What is the probability that you will win this lottery game? b. There are many variations of this game. The primary variation allows you to win if the four digits in your number are selected in any order as long as they are the same four digits as obtained by the lottery agency. For example, if you pick four digits making the number 1265, then you will win if \(1265,2615,5216,6521\), and so forth, are drawn. The variations of the lottery game depend on how many unique digits are in your number. Consider the following four different versions of this game. i. All four digits are unique (e.g., 1234 ) ii. Exactly one of the digits appears twice (e.g., 1223 or 9095 ) iii. Two digits each appear twice (e.g., 2121 or 5588 ) iv. One digit appears three times (e.g., 3335 or 2722 ) Find the probability that you will win this lottery in each of these four situations.

A random sample of 250 adults was taken, and they were asked whether they prefer watching sports or opera on television. The following table gives the two-way classification of these adults $$\begin{array}{lcc} \hline & \begin{array}{c} \text { Prefer Watching } \\ \text { Sports } \end{array} & \begin{array}{c} \text { Prefer Watching } \\ \text { Opera } \end{array} \\ \hline \text { Male } & 96 & 24 \\ \text { Female } & 45 & 85 \end{array}$$ a. If one adult is selected at random from this group, find the probability that this adult i. prefers watching opera ii. is a male iii. prefers watching sports given that the adult is a female iv. is a male given that he prefers watching sports \(\mathbf{v}\). is a female and prefers watching opera vi. prefers watching sports or is a male b. Are the events "female" and "prefers watching sports" independent? Are they mutually exclusive? Explain why or why not.

A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are asked whether or not they are happy with their majors. The following table gives the results of the survey. Assume that none of these 250 students is majoring in both areas. $$ \begin{array}{lcc} \hline & \text { Happy } & \text { Unhappy } \\ \hline \text { Psychology } & 80 & 20 \\ \text { Communication } & 115 & 35 \end{array} $$ a. If one student is selected at random from this group, find the probability that this student is i. happy with the choice of major ii. a psychology major iii. a communication major given that the student is happy with the choice of majon iv. unhappy with the choice of major given that the student is a psychology major v. a psychology major and is happy with that major vi. a communication major \(o r\) is unhappy with his or her major b. Are the events "psychology major" and "happy with major" independent? Are they mutually exclusive? Explain why or why not.

What is meant by two mutually exclusive events? Give one example of two mutually exclusive events and another example of two mutually nonexclusive events.
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