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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

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?

1994, the U.S. government held a lottery to issue 55000Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5million people who entered this lottery. Let G = won green card.

a. What was Renate’s chance of winning a Green Card? Write your answer as a probability statement.

b. In the summer of 1994, Renate received a letter stating she was one of 110,000finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card? Write your answer as a conditional probability statement. Let F = was a finalist.

c. Are G andF independent or dependent events? Justify your answer numerically and also explain why.

d. Are G and F mutually exclusive events? Justify your answer numerically and explain why.

Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55%prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6%of all Californians are Latino. In this problem, let: • C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

Are L and C mutually exclusive events? Show why or why not

A box is filled with several party favors. It contains 12

hats, 15 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(N).

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 two lines that touch each other on the table as in 1-2-3-4-5-6

b. Betting on three numbers in a line, as in 1-2-3

c. Betting on one number

d. Betting on four numbers that touch each other to form a square, as in 10-11-13-14

e. Betting on two numbers that touch each other on the table, as in 10-11or10-13

f. Betting on 0-00-1-2-3

g. Betting on 0-1-2;or0-00-2;or00-2-3
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