4. Probability
Basic Concepts of Probability
1:46 minutesProblem 4.c.3b
Textbook Question
Organ Donors USA Today provided information about a survey (conducted for Donate Life America) of 5100 adult Internet users. Of the respondents, 2346 said they are willing to donate organs after death. In this survey, 100 adults were surveyed in each state and the District of Columbia, and results were weighted to account for the different state population sizes.
b. Based on the poll results, what is the probability of randomly selecting an adult who is willing to donate organs after death?
Verified step by step guidance1
Step 1: Identify the total number of respondents in the survey. According to the problem, the total number of adult Internet users surveyed is 5100.
Step 2: Identify the number of respondents who are willing to donate organs after death. From the problem, this number is given as 2346.
Step 3: Recall the formula for probability. The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. Mathematically, this is expressed as: .
Step 4: Substitute the values into the formula. Here, the favorable outcomes are the 2346 respondents willing to donate organs, and the total outcomes are the 5100 respondents surveyed. The formula becomes: .
Step 5: Simplify the fraction to express the probability in its simplest form or as a decimal, if required. This will give the probability of randomly selecting an adult who is willing to donate organs after death.
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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 an adult who is willing to donate organs. The probability can be calculated by dividing the number of favorable outcomes (adults willing to donate) by the total number of outcomes (total surveyed adults).
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Sample Size
Sample size refers to the number of observations or respondents included in a survey or study. In this case, the sample size is 5100 adult Internet users. A larger sample size generally leads to more reliable results, as it better represents the population and reduces the margin of error in probability estimates.
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Weighted Results
Weighted results are adjustments made to survey data to ensure that the sample accurately reflects the population's characteristics. In this survey, results were weighted to account for different state population sizes, which helps to avoid bias and ensures that the findings are representative of the entire adult population in the USA.
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