4. Probability
Basic Concepts of Probability
1:50 minutesProblem 4.q.6
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 that developed flu.
Verified step by step guidance1
Step 1: Begin by identifying the total number of subjects in the experiment. Add all the values in the table: 14 (Developed Flu, Vaccine Treatment) + 1056 (Did Not Develop Flu, Vaccine Treatment) + 95 (Developed Flu, Placebo) + 437 (Did Not Develop Flu, Placebo).
Step 2: Calculate the total number of subjects who developed flu. Add the values from the 'Developed Flu' column: 14 (Vaccine Treatment) + 95 (Placebo).
Step 3: To find the probability of randomly selecting a subject who developed flu, divide the total number of subjects who developed flu (from Step 2) by the total number of subjects in the experiment (from Step 1).
Step 4: Express the probability as a decimal. Ensure the division result is rounded appropriately if necessary.
Step 5: Interpret the result. The probability represents the likelihood of randomly selecting a subject who developed flu from the entire group of 1602 subjects.
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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 developed the flu from the total number of subjects. The probability can be calculated by dividing the number of favorable outcomes (subjects who developed flu) by the total number of outcomes (total subjects).
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Experimental Design
Experimental design refers to the framework for conducting an experiment, including how subjects are assigned to treatment groups. In this case, the subjects are divided into two groups: those receiving the vaccine treatment and those receiving a placebo. Understanding the design helps in interpreting the results and assessing the effectiveness of the vaccine.
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Contingency Table
A contingency table is a data representation that displays the frequency distribution of variables, allowing for the analysis of the relationship between them. The provided table shows the number of subjects who developed or did not develop flu under two different treatments (vaccine and placebo). This format aids in calculating probabilities and understanding the impact of the vaccine.
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