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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
Chapter 3, Problem 3.2.27a

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)
a. Find the probability that all six have type O+ blood."

Verified step by step guidance
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Step 1: Understand the problem. We are tasked with finding the probability that all six randomly selected people of Asian descent in the United States have type O+ blood. This involves using the Multiplication Rule for independent events, as the blood type of one person does not affect the blood type of another.
Step 2: Identify the given probability. The probability that a single person of Asian descent has type O+ blood is given as 39%, which can be expressed as 0.39 in decimal form.
Step 3: Recognize the independence of events. Since the blood type of each person is independent of the others, the probability of all six having type O+ blood can be calculated by multiplying the probability for one person by itself six times.
Step 4: Write the formula for the probability. Using the Multiplication Rule, the probability that all six have type O+ blood is given by: P = (0.39)^6.
Step 5: Simplify the expression. To find the final probability, calculate the value of (0.39)^6. This involves raising 0.39 to the power of 6. Use a calculator or software to compute this value if needed.

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Key Concepts

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

Multiplication Rule of Probability

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this context, if the probability of one person having type O+ blood is 39%, the probability of multiple people having the same blood type can be calculated by multiplying the individual probabilities together.
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Multiplication Rule: Dependent Events

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the selection of one person does not influence the blood type of another selected person, allowing us to treat each selection as an independent event when calculating the overall probability.
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Probability of Multiple Independent Events

Probability Calculation

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. To find the probability that all six selected individuals have type O+ blood, we raise the individual probability (0.39) to the power of the number of individuals (6), reflecting the repeated independent trials.
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Probability From Given Z-Scores - TI-84 (CE) Calculator
Related Practice
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)

a. Find the probability that all four have type A+ blood."

Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

a. The person wears only contacts or only glasses.

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Textbook Question

Shuffle Play You use a shuffle playback feature to randomly play songs in a playlist. The playlist of 56 songs includes 15 instrumental songs.

a. What is the probability that the first three songs to play are instrumental songs? (Assume a song cannot be repeated.)

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Textbook Question

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

24. Knowing a Person Who Was Murdered In a sample of 11,771 children ages 2 to 17, 8% have lost a friend or relative to murder. Four children are selected at random. (Adapted from University of New Hampshire)

a. Find the probability that all four have lost a friend or relative to murder.

Textbook Question

U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census

Bureau)

a. Randomly selecting someone who is under 10 years old

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)

a. Find the probability that both probable voters would like entertainers to address social and political issues.