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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.2.30b
Chapter 3, Problem 3.2.30b

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
30. Standardized Test Scores According to a survey, 57.8% of college-seeking high school seniors say they have taken one of the standardized tests for potential college students. Of these, 35.6% say they do not plan to submit their score with their college applications. (Adapted from Niche)
b. Find the probability that a randomly selected college-seeking high school senior took one of the standardized tests and plans to submit this score with their college
applications.

Verified step by step guidance
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Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected college-seeking high school senior took one of the standardized tests AND plans to submit this score with their college applications. This involves using the Multiplication Rule for probabilities.
Step 2: Recall the Multiplication Rule. The rule states that the probability of two events A and B occurring together (denoted as P(A and B)) is given by P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.
Step 3: Define the events. Let event A be 'a student took one of the standardized tests' and event B be 'a student plans to submit their score with their college applications.' From the problem, P(A) = 57.8% = 0.578, and P(B|A) = 1 - 35.6% = 64.4% = 0.644 (since 35.6% do NOT plan to submit their scores).
Step 4: Apply the Multiplication Rule. Substitute the given probabilities into the formula: P(A and B) = P(A) * P(B|A). This becomes P(A and B) = 0.578 * 0.644.
Step 5: Interpret the result. The product from Step 4 will give the probability that a randomly selected college-seeking high school senior took one of the standardized tests AND plans to submit their score with their college applications. Perform the multiplication to find the final probability.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiplication Rule

The Multiplication Rule in probability states that the probability of two independent events occurring together is the product of their individual probabilities. This rule is essential for calculating the likelihood of combined events, especially when determining the probability of one event happening given that another event has already occurred.
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Probability of Multiple Independent Events

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this context, it helps in understanding the likelihood that a student who has taken a standardized test also plans to submit their scores, which is crucial for applying the Multiplication Rule effectively.
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Introduction to Probability

Joint Probability

Joint probability is the probability of two events happening at the same time. In this scenario, it involves calculating the probability that a college-seeking high school senior both took a standardized test and intends to submit their scores. This concept is vital for combining the probabilities derived from the Multiplication Rule and conditional probabilities.
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Introduction to Probability
Related Practice
Textbook Question

18. Rolling a Die You roll a die. Find the probability of each event.

b. Rolling a 2 or an odd number

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Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

b. Find the probability that neither probable voter would like entertainers to address social and political issues."

Textbook Question

Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.

7. Business Degrees The table shows the numbers of male and female students in the United States who received bachelor's degrees in business and nonbusiness fields in a recent year. (Source: National Center for Educational Statistics)

b. Find the probability that a randomly selected bachelor's degree-earning student received a business degree, given that the student is female.

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Textbook Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

28. Blood Types The probability that a Latinx American person in the United States has type A+ blood is 29%. Four Latinx American people in the United States are selected at random. (Source: American National Red Cross)

b. Find the probability that none of the four have type A+ blood.

Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. b. 333.3%

Textbook Question

22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the

probability of each event. (Adapted from Ipsos)

b. Randomly selecting a British adult who feels that the move has had a very negative impact on Great Britain