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Consider an experiment that consists of determining the type of job—either blue collar or white collar— and the political affiliation—Republican, Democratic, or Independent—of the 15 members of an adult soccer team.

How many outcomes are

(a) in the sample space?

(b) in the event that at least one of the team members is a blue-collar worker?

(c) in the event that none of the team members considers himself or herself an Independent?

Short Answer

Expert verified

(a) The outcomes in the sample space are615.

(b) The outcomes in the event that at least one of the team members is a

blue-collar worker are615-315.

(c) The outcomes in the event that none of the team members considers

himself or herself an Independent are

Step by step solution

01

Part (a) Step 1. Find the outcomes in the sample space.

Each member can have either two types of jobs - blue collared or white collared.

Further each member can be either Republican or Democratic or Independent.

So, there are three options. That means every member can have one of the2×3=6 categories.

The no. of members are15.

Hence, the sample space is615.

02

Part (b) Step 1. Find the  outcomes in the event that at least one of the team members is a blue-collar worker.

The possible no. of cases for the event that at least one of the team members is a blue collar worker means, we will exclude the cases that all the members are not blue collar from the total sample space.

So, we will consider the level of job type with only blue collar.

This means615-1×315.

Therefore, the outcomes in the event that at least one of the team members is a blue-collar worker are615-315.

03

Part (c) Step 1. Find the  outcomes in the event that none of the team members considers himself or herself an Independent..

The event that none of the team members considers himself or herself an independent means the 15 members are from either Republican or Democratic Party.

Therefore, the number of outcomes per members is2×2=4

The total members are15

Therefore, the total number of possible outcomes are415.

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Most popular questions from this chapter

The chess clubs of two schools consist of, respectively, 8and9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that

(a) Rebecca and Elise will be paired?

(b) Rebecca and Elise will be chosen to represent their schools but will not play each other?

(c) either Rebecca or Elise will be chosen to represent her school?

1. A cafeteria offers a three-course meal consisting of an entree, a starch, and a dessert. The possible choices are given in the following table:

Course
Choices
Entree
Chicken or roast beef
Starch
Pasta or rice or potatoes
Dessert
Ice cream or Jello or apple pie or a peach

A person is to choose one course from each category.

(a)How many outcomes are in the sample space?

(b)Let Abe the event that ice cream is chosen. How many outcomes are inA?

(c)Let Bbe the event that chicken is chosen. How many outcomes are inB?

(d)List all the outcomes in the eventAB.

(e)LetCbe the event that rice is chosen. How many outcomes are inC?

(f)List all the outcomes in the eventABC.

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