Textbook Question
34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)
Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.2.16
"Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.
16. A study found no significant association between the use of talc powder and the incidence of ovarian cancer in women. (Source: JAMA)"
Verified step by step guidance1
Step 1: Identify the two events described in the study. The first event is 'the use of talc powder,' and the second event is 'the incidence of ovarian cancer in women.'
Step 2: Understand the concept of independence in probability. Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event.
Step 3: Analyze the study's findings. The study states that there is 'no significant association' between the use of talc powder and ovarian cancer. This suggests that the probability of ovarian cancer does not change based on whether talc powder is used.
Step 4: Conclude whether the events are independent or dependent. Based on the study's findings, the events are independent because the use of talc powder does not influence the likelihood of ovarian cancer.
Step 5: Explain the reasoning. Independence is supported by the lack of a significant association, meaning the two events occur without influencing each other, as indicated by the study's results.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Independent and Dependent Events
In probability theory, independent events are those whose occurrence does not affect the probability of another event occurring. Conversely, dependent events are those where the occurrence of one event influences the probability of another. Understanding this distinction is crucial for analyzing the relationship between the use of talc powder and ovarian cancer incidence in the study.
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Statistical Association
Statistical association refers to a relationship between two variables where changes in one variable are related to changes in another. In the context of the study, a lack of significant association suggests that the use of talc powder does not correlate with the incidence of ovarian cancer, indicating that the two events may be independent.
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Significance Testing
Significance testing is a statistical method used to determine if the results of a study are likely due to chance or if they reflect a true effect. In this study, the finding of 'no significant association' implies that the evidence is insufficient to conclude that talc powder use affects ovarian cancer risk, which is essential for interpreting the results and their implications.
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Related Practice
Textbook Question
"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.
13. Rolling a six-sided die and then rolling the die a second time so that the sum of the two rolls is five"
Textbook Question
Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.
71. What is the probability that all three children are girls?
Textbook Question
According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
37. P(A) = 73%, P(A') = 17%, P(B|A) = 46% , and P(B|A') = 52%
Textbook Question
20. Skating Eight people compete in a short track speed skating race. Assuming that there are no ties, in how many different orders can the skaters finish?
Textbook Question
97. Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum.
a. List all of the possible sums and determine the probability of rolling each sum.
b. Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling
each sum.
c. Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.