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Chapter 3: Q. 106 (page 227)

Suppose that a member of the USSenate is randomly selected. What is the probability that the senator is up for reelection in November 2014, knowing that this senator is a Republican?

Short Answer

Expert verified

Considering that the senator is a Republican, there is a 1337possibility that he or she will be up for reelection in November localid="1649665036316" 2014.

Step by step solution

01

Step: 1 Conditional probability:

The potential of an event or outcome occurring dependent on the existence of a preceding event or outcome is known as conditional probability. It's computed by multiplying the likelihood of the previous occurrence by the probability of the next, or conditional, event.

02

Step: 2 Finding probability:

We need to calculate the conditional probability of the senator being up for reelection in November 2014, assuming that he is a Republican.

There are 37Republicans in the House of Representatives, and 13of them are up for reelection in November 2014. As a result, the probability is calculated as follows:

P=1337.

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Most popular questions from this chapter

Use the following information to answer the next ten exercises. 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.

Find P(L).

In a bag, there are six red marbles and four green marbles. The red marbles are marked with the numbers 1, 2, 3,4, 5, and 6. The green marbles are marked with the numbers 1, 2, 3, and 4.

• R = a red marble

• G = a green marble

• O = an odd-numbered marble

• The sample space is S = {R1, R2, R3, R4, R5, R6, G1, G2, G3, G4}.

S has ten outcomes. What is P(G AND O)?

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 12exercises. The graph shown is based on more than 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.

What is the range of the data?

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?
See all solutions

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