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Chapter 3: Q. 104 (page 227)

Use the information in the Table \(3.19\) to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the US Senate in June 2012 , and when they are up for reelection.

104. What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014 ?

Short Answer

Expert verified

The probability that a randomly selected senator is a Republican or is up for reelection in November 2014 is5767.

Step by step solution

01

Step1:Definition of probability

If an experiment can generate N mutually exclusive and equally likely outcomes, n of which are favorable to the occurrence of event A, then the probability of A is denoted by P (A) and is defined as the ratio n N. As a result, the probability of A is given by

02

Step2:The probability that a randomly selected senator is a Republican 

There are 67 members in total, with57of them being Republicans or running for reelection in November 2014. As a result, the probability is given by:

P=5767

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Most popular questions from this chapter

Approximately 281,000,000people over age five live in the United States. Of these people, 55,000,000speak a language other than English at home. Of those who speak another language at home, 62.3%speak Spanish.

Let:E = speaks English at home; 贰鈥� = speaks another language at home; S = speaks Spanish;

Finish each probability statement by matching the correct answer.

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

Find P(N).

A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:

a. Let F = the event of getting the white ball twice.

b. Let G = the event of getting two balls of different colors.

c. Let H = the event of getting white on the first pick.

d. Are F and G mutually exclusive?

e. Are G and H mutually exclusive?

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E|M) mean in words?

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E OR M) mean in words?
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