CHAPTER 9: ESSENTIAL PROBABILITY RULES

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Questions and Answers

What is the probability that a randomly selected adult American male is either overweight or obese?

  • 0.30
  • 0.29
  • 0.70 (correct)
  • 0.41

What is the probability that a randomly selected adult American male has a weight that is considered healthy?

  • 0.29 (correct)
  • 0.11
  • 0.59
  • 0.71

Based on the information provided, what is the probability that a randomly selected adult American male is neither overweight nor obese?

  • 0.71
  • 0.41
  • 0.29 (correct)
  • 0.59

What is the probability that a reported case of rabies in Florida in 2011 is not a raccoon?

<p>0.43 (A)</p>
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What is the probability that a reported case of rabies in Florida in 2011 is either a bat or a fox?

<p>0.26 (C)</p>
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If an event has a probability of 0.75, what is the probability that the event does not occur?

<p>0.25 (A)</p>
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If two events, A and B, are mutually exclusive (they cannot happen at the same time) and P(A) = 0.3 and P(B) = 0.4, what is the probability of either A or B occurring?

<p>0.7 (A)</p>
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Which of the following statements is NOT true regarding probability?

<p>The sum of the probabilities of all possible outcomes in a sample space must be equal to or less than 1. (B)</p>
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If an event has a probability of 0, what does this imply?

<p>The event will never occur. (B)</p>
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Two events are said to be independent if:

<p>The occurrence of one event does not affect the probability of the other event. (C)</p>
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What is the probability that a randomly selected high school student was physically active for at least 60 minutes on exactly 3 days out of the past 7?

<p>0.11 (C)</p>
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What is the probability that a high school student was physically active for at least 60 minutes on at least one day of the past 7?

<p>0.11 (A)</p>
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What is the probability that a randomly selected high school student was NOT physically active for at least 60 minutes on any of the past 7 days?

<p>0.15 (B)</p>
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How many high school students out of the 15,000 surveyed would you expect to report being physically active for at least 60 minutes on 5 days out of the past 7?

<p>1800 (C)</p>
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What is the probability that a randomly selected high school student was physically active for at least 60 minutes on at least 4 days out of the past 7?

<p>0.39 (D)</p>
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Based on the text, what is the relationship between the proportion of 0s in the first 50 digits of a random digit table and the true probability of a 0 occurring?

<p>The proportion is an approximation of the true probability, based on a limited sample size. (A)</p>
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What does simulating 200 digits in the Probability applet with a probability of heads set to 0.1 represent?

<p>An experimental simulation of the distribution of 0s in a larger set of random digits. (A)</p>
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What is the main point the author is trying to convey about probability in the paragraph starting with 'Probability says...'?

<p>Probability allows us to quantify how likely an event is to occur, with specific numerical values representing different likelihoods. (C)</p>
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Based on the provided information, which of the following probabilities would be most likely to represent an event that will occur more often than not?

<p>0.6 (A)</p>
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Why does the text state that obtaining the medical records of 100,000 males will not necessarily result in exactly 13 individuals diagnosed with hemophilia?

<p>Because the probability of hemophilia applies to a population, not to specific individuals within that population. (D)</p>
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Flashcards

Probability 0

An event with probability 0 never occurs.

Probability 1

An event with probability 1 occurs on every trial.

Probability 0.5

An event with probability 0.5 occurs in half of all trials.

Sum of Probabilities

The sum of the probabilities of all possible outcomes must equal 1.

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Complement Rule

The probability that an event does not occur is 1 minus its probability of occurrence.

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Random Digits

Digits generated randomly, each having a 0.1 probability for being a '0'.

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Proportion of 0s

Estimate of '0s' in a sample of random digits, based on a smaller subset.

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Event Likelihood Statements

Statements that describe the likelihood of an event occurring, like certain or impossible.

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Simulation in Probability

An experimental method to replicate random events to estimate probabilities.

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Discrete Probability Model

A model where outcomes are distinct, with assigned probabilities for each outcome.

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Legitimate Probability Model

A probability model where all probabilities are non-negative and sum to 1.

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Event X < 7

The event where the number of physically active days is less than 7.

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P(X < 7)

The probability of less than 7 days of physical activity, calculated from the model.

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At least one day active

The event where X is greater than or equal to 1, indicating physical activity on at least one day.

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Obesity Statistics

29% of American males aged 18+ are obese according to the Census Bureau.

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Healthy Weight Percentage

29% of adult American males have a healthy weight.

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Weight Higher than Healthy

41% of American males and 56% of American females have a weight higher than healthy.

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Rabies Probability

The probability of documented rabies cases by species, with raccoons at 0.57.

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Probability Not a Raccoon

The probability that a reported case of rabies is not a raccoon is 0.43.

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Study Notes

Probability Rules

  • Probability is a number between 0 and 1 (inclusive)
  • The sum of probabilities for all possible outcomes is 1
  • If two events are mutually exclusive, the probability that one or the other occurs is the sum of their individual probabilities.

Random Variables

  • A random variable is a variable whose value is a numerical outcome of a random phenomenon
  • Discrete random variables take only specific values
  • Continuous random variables can take any value in an interval

Probability Distributions

  • For a discrete random variable, the probability distribution lists the possible outcomes and their associated probabilities.
  • For a continuous random variable, the probability distribution uses a density curve, where areas under the curve represent probabilities.

Independent Events

  • Two events are independent if the outcome of one event does not affect the probability of the other event.

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Related Documents

Baldi et al. Chapter 9 (3rd ed) PDF - Introducing Probability

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