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Chapter 3: Q. 108 (page 227)

Use the information in the Table3.19to answer the next eight exercises. The table shows the political party affiliation of each of localid="1649516803996" 67members of the US Senate In June localid="1649516807155" 2012. and when they are up freelection.

The events "Other" and "Up for reelection in November localid="1649516811372" 2016' are

a. mutually exclusive.

b. independent.

c. both mutually exclusive and independent.

d. neither mutually exclusive nor independent

Short Answer

Expert verified

In November 2016, the events Other and Up for reelection are mutually exclusive.

As a result, mutually exclusive is the correct answer.

Step by step solution

01

Given

The table shows the political party affiliation of each of 67members of the US Senate In June 2012. and when they are up reelection.

02

Finding the probability of event Other and Is up for reelection in 2016

The total as:

Events A and B are mutually exclusive if the probability of event AAND Bequals 0.

Finding the probability of event Other and Is up for reelection in 2016:

P=067=0

Thus, we can conclude that events are mutually exclusive.

If events A and B are mutually exclusive, then they cannot be independent. That is because, if they are mutually exclusive, they cannot happen at the same time. If we know that B happened, then we immediately know that A didn't. Thus:

P(A鈭�B)=0鈮�P(A)

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Most popular questions from this chapter

Use the following information to answer the next 12exercises. The graph shown is based on more than localid="1648902668215">170,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

If we know an Emotional Health Index Score is 81.5 or more, what is the probability that it is 82.7.

Suppose that one person from the study is randomly selected. Find the probability that person smoked 11to20 cigarettes per day

In words, explain what it means to pick one person from the study who is 鈥淛apanese American OR smokes21to30 cigarettes per day.鈥� Also, find the probability.

Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area.

Let B = the event of landing on blue.

Let R = the event of landing on red.

Let G = the event of landing on green.

Let Y = the event of landing on yellow.

If you land on Y, you get the biggest prize. Find P(Y).

Use the following information to answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38numbers, and each number is assigned to a color and a range.

Compute the probability of winning the following types of bets:

a. Betting on a color

b. Betting on one of the dozen groups

c. Betting on the range of numbers from 1to18

d. Betting on the range of numbers19-36

e. Betting on one of the columns

f. Betting on an even or odd number (excluding zero)
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