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Chapter 4: Problem 3

A box contains three items that are labeled \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). Two items are selected at random (without replacement) from this box. List all the possible outcomes for this experiment. Write the sample space \(S .\)

Short Answer

Expert verified
The sample space \(S\) for the random selection of two items from the box is \(\{AB, AC, BC\}\)

Step by step solution

01

Identify the available items

There are three items available in the box labeled A, B, and C.
02

List the possible outcomes

Start selecting items two at a time. Without replacement means once an item is selected, it won't be put back in the box for the second selection. The possible outcomes when two items are being selected from three are AB, AC, and BC.
03

Define the sample space

The sample space \(S\) of an experiment is defined as the set of all possible outcomes. For this case, \(S = \{AB, AC, BC\}\).

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Most popular questions from this chapter

Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two- way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as. or worse off than their parents. $$\begin{array}{lccc} \hline & \begin{array}{c} \text { Less Than } \\ \text { High School } \end{array} & \begin{array}{c} \text { High } \\ \text { School } \end{array} & \begin{array}{c} \text { More Than } \\ \text { High School } \end{array} \\ \hline \text { Better off } & 140 & 450 & 420 \\ \text { Same as } & 60 & 250 & 110 \\ \text { Worse off } & 200 & 300 & 70 \\ \hline \end{array}$$ a. Suppose one adult is selected at random from these 2000 adults. Find the following probabilities. i. \(P\) (better off and high school) ii. \(P(\) more than high school and worse off ) b. Find the joint probability of the events "worse off" and "better off." Is this probability zero? Explain why or why not.

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