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.

Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

검증된 단계별 안내

Step 1: Calculate the total number of subjects in the study by summing all the values in the table. Add the number of subjects who developed flu and did not develop flu for both the vaccine treatment and placebo groups.

Step 2: Identify the total number of subjects who developed flu by summing the 'Developed Flu' column for both the vaccine treatment and placebo groups.

Step 3: Calculate the probability of selecting one subject who developed flu. This is done by dividing the total number of subjects who developed flu by the total number of subjects in the study.

Step 4: Since the selection is without replacement, calculate the probability of selecting a second subject who developed flu after the first one has been selected. Subtract 1 from the total number of subjects who developed flu and divide by the total number of subjects minus 1.

Step 5: Multiply the probabilities from Step 3 and Step 4 to find the overall probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 involves calculating the chance of selecting subjects who developed flu from a given population. Understanding how to compute probabilities, especially in scenarios involving combinations and selections, is crucial for answering the question.

Without Replacement

Selecting without replacement means that once an item is chosen from a set, it is not returned to that set for subsequent selections. This affects the total number of items available for the next selection, which in turn influences the probability calculations. In this case, the probability of selecting two subjects who developed flu must account for the reduced pool of subjects after the first selection.

Contingency Table

A contingency table is a type of data representation that displays the frequency distribution of variables, allowing for easy comparison of different groups. In this scenario, the table shows the number of subjects who developed flu versus those who did not, categorized by treatment type (vaccine vs. placebo). Analyzing this table is essential for determining the probabilities needed to answer the question.