Two-Way Tables
Two-way tables, also known as contingency tables, are a fundamental tool in statistical analysis, providing a systematic way to organize and interpret categorical data. These tables present data across two dimensions, allowing for the examination of relationships between two categorical variables. By displaying frequencies or proportions within intersecting categories, two-way tables offer insights into patterns, associations, and dependencies within the data. Understanding how to construct and interpret two-way tables is essential for various fields, including social sciences, healthcare, and market research, where analyzing relationships between variables is crucial for informed decision-making.
Questions
- Two dice are rolled. The first die shows "1," so its outcome is known. However, the other die rolls under the table where it cannot be seen. What is the probability that both of the dice show "1"?
- What is the probability that the next person will be assigned an aisle seat?
- Consider a two-way table that summarizes age and ice cream preference. Of the children, 7 prefer vanilla, 12 prefer chocolate, and 3 prefer butter pecan. Of the adults, 10 prefer vanilla, 31 prefer chocolate, and 8 prefer butter pecan. What is the joint probability that a randomly selected person is a child who prefers chocolate?
- What is a joint probability in a two-way table?
- What is a conditional probability in a two-way table?
- Consider a two-way table that summarizes age and ice cream preference. Of the children, 7 prefer vanilla, 12 prefer chocolate, and 3 prefer butter pecan. Of the adults, 10 prefer vanilla, 31 prefer chocolate, and 8 prefer butter pecan. What is the conditional probability that a person prefers vanilla, GIVEN THAT the person is an adult?
- Consider a two-way table that summarizes age and ice cream preference. Of the children, 7 prefer vanilla, 12 prefer chocolate, and 3 prefer butter pecan. Of the adults, 10 prefer vanilla, 31 prefer chocolate, and 8 prefer butter pecan. What is the probability that a randomly selected individual is a child, GIVEN THAT the person prefers butter pecan?
- Consider a two-way table that summarizes age and ice cream preference. Of the children, 7 prefer vanilla, 12 prefer chocolate, and 3 prefer butter pecan. Of the adults, 10 prefer vanilla, 31 prefer chocolate, and 8 prefer butter pecan. Are the events "chocolate" and "child" independent? Why or why not?
- What is a two-way table?
- How do you calculate marginal, joint, and conditional probabilities from a two-way table?
- How can we divide the salary data #{199,200,202,203,207,208,208,209,210,210,210,210,212,213,214,215,217,218,218,221}# in six classes?
- How does probability relate to the punnett square and the offspring?
- How many different distinguishable horizontal arrangements of 7 identically shaped balls are there if 2 are blue, 3 are red, and 2 are yellow?
- In the box are 30 lottery tickets. 5 of them are happy. 7 tickets are being fetched. In how many cases, there will be 2 happy tickets?
- Conditional probability using two-way tables?
- Two 6-sided dice are rolled. What is the probability that their results differ by 1?
- What's the probability of rolling a 9 or higher using two fair standard dice?
- A hall has 'n' doors. Suppose that 'n' people each choose any door at random to enter the hall. a) In how many ways can this be done? b) What is the probability that at least 1 door will not be chosen by any of the people?
- A case of wine contains 12 bottles, of which two are improperly sealed and spoiled. If two bottles are randomly selected from the case, what is the probability that both are spoiled?
- In how many ways can four men and four women be seated around a circular table if each man must be flanked by two women?