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  Problem: Analyzing Student Preferences for Studying A university conducted a survey among 200 students to determine their preferred study environment and whether they prefer studying alone or in groups. The results are summarized in the following two-way table: Study Environment Study Alone Study in Groups Total Library 50 30 80 Home 60 40 100 Coffee Shop 10 10 20 Total 120 80 200   What is the probability that a randomly selected student prefers to study alone and studies at home?     

  The number of movies watched by each person in a month is an example of :

An urn contains 4 red balls, 5 blue balls, and 3 green balls. Three balls are selected one at a time without replacement. What is the probability that at least one selected ball is blue? ( round to 4 decimal places)

**In a class , 30% of the students play tennis, and 50%  play badminton. If 15% of the students play both tennis and badminton, what is the probability that a randomly selected student plays tennis or badminton?** ( no need to round)

A school library has 12 fiction books and 8 nonfiction books on a display shelf. Two books are selected at random without replacement. What is the probability that both selected books are nonfiction books? ( round to four decimal places)

**Problem: Classifying a Dataset as Right Skewed or Left Skewed or Neither** Instructions: You are given a dataset of test scores. Your task is to analyze the distribution of the scores and determine whether the dataset is right skewed, left skewed, or neither. Once you have examined the dataset, provide your conclusion about its skewness. Dataset: Test Scores | Student | Score | |———|——-| | 1       | 45    | | 2       | 50    | | 3       | 55    | | 4       | 60    | | 5       | 65    | | 6       | 70    | | 7       | 60   | | 8       | 100    |

A certification exam has a pass rate of 82%. Four students are selected independently at random to take the exam. What is the probability that none of the four students pass the exam? ( three decimal places)

**A study was done to ascertain the effectiveness of a diet program. Two groups of people (on diet and not on diet) were followed to see how many in each group lost weight. The results are summarized in the table below:** |                | On Diet | Not on Diet ||—————-|———|————-|| Lost Weight    | 120     | 80          || Did Not Lose Weight | 180 | 120        | What is the probability that if a person in this study is randomly selected, that person did not lose weight? ( no need to round)

**A study was done to ascertain the effectiveness of a new exercise program. Two groups of people (following the program and not following the program) were followed to see how many in each group improved their fitness level. The results are summarized in the table below:** |                  | Following Program | Not Following Program ||——————|——————-|———————–|| Improved Fitness | 150                | 100                   || No Improvement   | 100               | 150                   | What is the probability that if a person in this study is randomly selected, that person improved their fitness and was following the program? ( no need to round)

If expenses are paid in cash (assume when they pay the cash, the expense is incurred)