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In contract negotiations between a local government agency and its workers, it is estimated that there is a 50% chance that an agreement will be reached on the salaries of the workers. It is estimated that there is a 70% chance that there will be an agreement on the insurance benefits. There is a 20% chance that no agreement will be reached on either issue. What is the probability that an agreement will be reached on both issues?

In contract negotiations between a local government agency and its workers, it is estimated that there is a 50% chance that an agreement will be reached on the salaries of the workers. It is estimated that there is a 70% chance that there will be an agreement on the insurance benefits. There is a 20% chance that no agreement will be reached on either issue. What is the probability that an agreement will be reached on both issues?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Probability in Contract Negotiations In the context of contract negotiations between a local government agency and its workers, several probabilities are estimated concerning agreement outcomes: - There is a **50% chance** that an agreement will be reached on the salaries of the workers. - There is a **70% chance** that an agreement will be reached on the insurance benefits. - There is a **20% chance** that no agreement will be reached on either issue. #### Question: What is the probability that an agreement will be reached on both issues? --- To solve this problem, we need to use the principles of probability, particularly the concept of joint probability for two independent events. Here, we consider: - Let \( P(S) \) be the probability of reaching an agreement on salaries. - Let \( P(I) \) be the probability of reaching an agreement on insurance benefits. Given: - \( P(S) = 0.50 \) - \( P(I) = 0.70 \) - \( P(\text{No Agreement}) = 0.20 \) We need to find the probability that an agreement will be reached on both issues, \( P(S \cap I) \). This scenario involves understanding complementary probabilities and the principle of inclusion-exclusion. The complementary probabilities are: - Probability of not reaching agreement on salaries, \( P(\text{Not } S) = 1 - P(S) = 1 - 0.50 = 0.50 \) - Probability of not reaching agreement on insurance benefits, \( P(\text{Not } I) = 1 - P(I) = 1 - 0.70 = 0.30 \) Using these, we calculate : - Probability of no agreement on at least one issue: \( P(\text{Not Agreed on Both}) = P(\text{No Agreement}) \). Given: \( P(\text{Not } S \cup \text{Not } I) = 0.20 \), Thus: \( P((S \cap I)^) = 0.20 \), Using Complement Rule: \( P(S \cap I) = 1 - 0.20 = 0.80 - (\text{Part for complementary })) = .... \) In advanced probability, define \(P(\text{Whole}) and both \ P (\cap I)...(For complex steps and other calculations, ensure classes teach... }\ ... The final
Transcribed Image Text:### Probability in Contract Negotiations In the context of contract negotiations between a local government agency and its workers, several probabilities are estimated concerning agreement outcomes: - There is a **50% chance** that an agreement will be reached on the salaries of the workers. - There is a **70% chance** that an agreement will be reached on the insurance benefits. - There is a **20% chance** that no agreement will be reached on either issue. #### Question: What is the probability that an agreement will be reached on both issues? --- To solve this problem, we need to use the principles of probability, particularly the concept of joint probability for two independent events. Here, we consider: - Let \( P(S) \) be the probability of reaching an agreement on salaries. - Let \( P(I) \) be the probability of reaching an agreement on insurance benefits. Given: - \( P(S) = 0.50 \) - \( P(I) = 0.70 \) - \( P(\text{No Agreement}) = 0.20 \) We need to find the probability that an agreement will be reached on both issues, \( P(S \cap I) \). This scenario involves understanding complementary probabilities and the principle of inclusion-exclusion. The complementary probabilities are: - Probability of not reaching agreement on salaries, \( P(\text{Not } S) = 1 - P(S) = 1 - 0.50 = 0.50 \) - Probability of not reaching agreement on insurance benefits, \( P(\text{Not } I) = 1 - P(I) = 1 - 0.70 = 0.30 \) Using these, we calculate : - Probability of no agreement on at least one issue: \( P(\text{Not Agreed on Both}) = P(\text{No Agreement}) \). Given: \( P(\text{Not } S \cup \text{Not } I) = 0.20 \), Thus: \( P((S \cap I)^) = 0.20 \), Using Complement Rule: \( P(S \cap I) = 1 - 0.20 = 0.80 - (\text{Part for complementary })) = .... \) In advanced probability, define \(P(\text{Whole}) and both \ P (\cap I)...(For complex steps and other calculations, ensure classes teach... }\ ... The final
The image displays a series of four radio buttons, each associated with a decimal number. The radio buttons are used for selection and typically appear in multiple-choice questions. The options are as follows: - 0.8 - 0.1 - 0.4 - 0.3 Each number has an empty circle next to it, indicating that no selection has been made. This formatting is often used in quizzes, surveys, or forms where a respondent is required to choose one option from a list of possible answers.
Transcribed Image Text:The image displays a series of four radio buttons, each associated with a decimal number. The radio buttons are used for selection and typically appear in multiple-choice questions. The options are as follows: - 0.8 - 0.1 - 0.4 - 0.3 Each number has an empty circle next to it, indicating that no selection has been made. This formatting is often used in quizzes, surveys, or forms where a respondent is required to choose one option from a list of possible answers.
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