# Probability with a Table

You are taking two courses during winter session, math and history, and your subjective assessment of your performance is

Event Probability

fail both courses .05

fail math (irrespective of whether or not you fail history as well) .15

fail history (irrespective of whether or not you fail math as well) .08

Let's develop a joint-probability table to analyze this problem (the letters A - H represent probability values. For example, A is the probability of failing both math and history; B is the probability of failing math and passing history; while C is the sum of A and B, and represents the probability of failing math).

fail history pass history row sum

fail math A B C

pass math D E F

column sum G H

a) (3 pts.) What does C + F equal?

b) (3 pts.) What does A + B + D + E equal?

c) (12 pts) What is the probability of failing math only (that is, you fail math but pass history)?

d) (12 pts) What is the probability of passing either course?

Please assist with the attached problem.

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#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.

Contingency Tables and Probablity: Cereal will be high calorie, high fiber

See attached template.

Using the Cereal worksheet (which we used in the Week 2 Lab for Linear Regression Analysis), the Calorie variable was recoded into "high calorie" and "low calorie" categories. We used 120 calories per serving as the break point (greater than or equal to 120 is "high calorie").

A contingency table was created inside the Cereal worksheet showing the breakdown of fiber and how it relates to calorie content. Use the contingency table to help answer the following probability questions. Write your answers inside the Week 4 Lab Template. You do not need to copy-and-paste anything from Excel.

Suppose one type of cereal is randomly selected.

1. What is the probability that the cereal would be high calorie? In other words, what is P(high calorie)?

2. What is the probability that the cereal would be high fiber? In other words, what is P(high fiber)?

3. What is the probability that a cereal would both high calorie and high fiber? In other words, what is P(high calorie and high fiber)?

4. What is the probability that a cereal would either high calorie or high fiber? In other words, what is P(high calorie or high fiber)?

5. What is the probability that a cereal would be high calorie, given that it is high fiber? In other words, what is P(high calorie, given high fiber)?

6. What is the probaility that a cereal would be high calorie, given that is is low fiber? In other words, what is P(high calorie, given low fiber)?

7. Regarding Questions 5 and 6, how might you interpret this information as a consumer?

8. Using the simple test of independence, decide if the events high calorie and high fiber are independent or dependent. Show your work.

9. Discuss how the Excel command "countif" was used in the table above. Why were the ranges (such as f2:f23) used as they were?

Place your answers inside the Week 4 Lab Template for submission. Be sure to follow the directions in the template.

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