Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

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1:58 minutes

Problem 4.q.8

Textbook Question

In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.

If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 who had the vaccine treatment and developed flu.

Verified step by step guidance

Step 1: Identify the total number of subjects in the experiment. Add all the values in the table: 14 (Vaccine Treatment, Developed Flu) + 1056 (Vaccine Treatment, Did Not Develop Flu) + 95 (Placebo, Developed Flu) + 437 (Placebo, Did Not Develop Flu).

Step 2: Focus on the specific group mentioned in the problem: subjects who had the vaccine treatment and developed flu. From the table, this corresponds to the value 14.

Step 3: Calculate the probability by dividing the number of subjects in the specified group (14) by the total number of subjects (calculated in Step 1). Use the formula: $ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} $.

Step 4: Express the probability in decimal form. Ensure the division result is converted to a decimal.

Step 5: Verify the calculation by double-checking the values from the table and ensuring the probability is correctly expressed in decimal form.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting a subject who received the vaccine treatment and developed flu. The probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes.

Favorable Outcomes

Favorable outcomes are the specific results that we are interested in when calculating probability. In this case, the favorable outcome is the number of subjects who received the vaccine treatment and developed flu, which is 14. Understanding favorable outcomes is crucial for accurately determining the probability of an event.

Total Outcomes

Total outcomes refer to the complete set of possible results in a probability scenario. Here, the total number of subjects is 1602, which includes both those who received the vaccine and those who received the placebo. Knowing the total outcomes is essential for calculating the probability, as it serves as the denominator in the probability formula.

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