Probability Quiz. 1. An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?
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2.Consider the experiment of tossing a coin two times. Use H to denote a head and T to denote a tail.
a. Select a tree diagram for the experiment.
b. List the experimental outcomes in such way: (H),(H,H) or (H,H,H). c. What is the probability for each experimental outcome (to 3 decimals)? The outcomes are , so the probability of each outcome is (are) (if outcomes are not equally likely then enter each probability separated with commas) . |
3. Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
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4. Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this question (CBS News website, December, 2014). Consider the responses by age groups shown below.
a. What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? c. For a randomly selected respondent, what is the probability that a respondent answers yes (to 3 decimals)? d. Based on the survey results, does there appear to be a difference between ages 18-29 and 30+ regarding concern over global warming? The input in the box below will not be graded, but may be reviewed and considered by your instructor. |
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5. A survey of magazine subscribers showed that 45.2% rented a car during the past 12 months for business reasons, 55% rented a car during the past 12 months for personal reasons, and 20% rented a car during the past 12 months for both business and personal reasons.
Round your answers to three decimal places. a. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? b. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons? |
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6. Suppose that we have two events, A and B, with P(A) = .50, P(B) = .50, and P(A ∩ B) = .20.
a. Find P(A | B) (to 4 decimals). b. Find P(B | A) (to 4 decimals). c. Are A and B independent? Why or why not? because P(A | B) is P(A). |
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7. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.3 and P(B) = 0.7.
a. What is P(A B)? b. What is P(A | B)? c. Is P(A | B) equal to P(A)? Are events A and B dependent or independent? d. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate? Use the probability information in this problem to justify your answer. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? |
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8. The prior probabilities for events A 1 and A 2 are P(A 1) = .50 and P(A 2) = .50. It is also known that P(A 1 A 2) = 0. Suppose P(B | A 1) = .10 and P(B | A 2) = .06.
a. Are events A 1 and A 2 mutually exclusive? b. Compute P(A 1 B) (to 4 decimals). Compute P(A 2 B) (to 4 decimals). c. Compute P(B) (to 4 decimals). d. Apply Bayes’ theorem to compute P(A 1 | B) (to 4 decimals). Also apply Bayes’ theorem to compute P(A 2 | B) (to 4 decimals). |
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9. About fifty-three percent of Americans use social media and other websites to voice their opinions about television programs. Below are the results of a survey of 1,331 individuals who were asked if they use social media and other websites to voice their opinions about television programs.
a. Show a joint probability table (to 4 decimals).
b. What is the probability a respondent is female (to 4 decimals)? c. What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female (to 4 decimals)? d. Let F denote the event that the respondent is female and A denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent? Explain. Since the numbers equal the events are said to be . |
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