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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. In words, what is C|L?

Short Answer

Expert verified
C|L is the probability that a Latino Californian voter prefers life in prison without parole.

Step by step solution

01

Understanding the Notation

In this problem, we are tasked with interpreting the notation \( C|L \). This notation reads as "C given L," which in probability terms means the probability that a Californian registered voter prefers life in prison without parole over the death penalty, given that the voter is Latino.
02

Breaking Down the Problem

We are given the following information:- 48% of all California registered voters overall prefer life in prison without parole (C).- 55% of Latino California registered voters prefer life in prison without parole (L).- 37.6% of all Californian voters are Latino.From this, we want to find what \( C|L \) represents in words.
03

Interpreting C|L in Context

The expression \( C|L \) specifically refers to the probability that a Latino Californian, chosen at random, prefers life in prison without parole over the death penalty. Since we know that among Latino voters, 55% prefer life in prison without parole, \( C|L \) reflects this preference specifically among Latino voters.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Probability Notation
Probability notation can seem complex at first, but with a little practice, it becomes more intuitive. A common notation used is the conditional probability notation, often expressed as \( C|L \). This signifies the probability of event \( C \) occurring, given that \( L \) has already occurred. In simpler terms, it's how likely one thing is to happen if we know something else is true.
\( C|L \) is read as "C given L". In this scenario, \( C \) is the event "a registered voter prefers life in prison without parole over the death penalty."
\( L \) is the particular demographic marker "being a Latino California registered voter."
So, \( C|L \) answers the question: if we know a voter is Latino, what is the probability that they prefer life in prison without parole?
Such notation is very useful in statistics and data analysis because it helps break down complex problems into understandable parts.
Decoding Voter Preferences
In statistical terms, voter preferences refer to the frequency with which different voter groups support certain opinions or options. Understanding this requires analyzing collected data.
In the current context, 48% of all Californian registered voters prefer life in prison without parole over the death penalty. This general statistic shows a significant portion of the population leaning towards this option. However, preferences can vary significantly across demographic groups.
When we focus on Latino California voters, the data indicates that 55% prefer life in prison without parole. This information demonstrates a stronger preference among Latino voters for this alternative compared to the general voting population. Identifying and understanding these differences in voter preferences is crucial for political analysts, allowing them to predict voting outcomes and tailor speeches and campaigns.
Latino Demographic in Statistics
The Latino demographic in California plays a vital role in understanding voter patterns and preferences. This group represents 37.6% of all Californian registered voters, which means their collective preference can significantly influence election outcomes and policy decisions.
The statistics show that within this group, there's a slightly higher preference for life in prison without parole over the death penalty, at 55%. This figure is important for political strategists and policymakers, as it highlights the Latino community’s priority issues.
  • Understand the significance of Latino preferences as they account for a substantial share of the electorate.
  • Recognize that nuanced differences exist in preferences between Latinos and the general population.
By analyzing this demographic's preferences, campaigns can be better tailored to address their concerns and priorities, thereby fostering more inclusive and effective political strategies.

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Most popular questions from this chapter

A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin. a. List the sample space. b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A). c. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification. d. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.

An experiment consists of first rolling a die and then tossing a coin. a. List the sample space. b. Let A be the event that either a three or a four is rolled first, followed by landing a head on the coin toss. Find P(A). c. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.

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 six exercises. A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange. Let B = the event of getting a blue jelly bean Let G = the event of getting a green jelly bean. Let O = the event of getting an orange jelly bean. Let P = the event of getting a purple jelly bean. Let R = the event of getting a red jelly bean. Let Y = the event of getting a yellow jelly bean. Find P(G)

Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. Let G1 = first card is green Let G2 = second card is green a. Draw a tree diagram of the situation. b. Find P(G1 AND G2). c. Find P(at least one green). d. Find P(G2|G1).

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