A long-term care facility has 500 residents. Among these residents, 200 have dementia, 150 have physical disabilities, and 75 have both dementia and a physical disability. How is the probability of a resident having either dementia or a physical disability but not both calculated?
To find the probability of a resident having either dementia or a physical disability but not both, calculate 200/500 + 150/500 - 75/500.
This calculation uses the principle of inclusion-exclusion to avoid double-counting the residents who have both conditions. By adding the probabilities of each condition and subtracting the probability of both, we accurately determine the probability of having either condition individually.
This option incorrectly suggests that the probability of having either condition is found by taking the complement of the sum of the probabilities of all three groups. This is not how probabilities for mutually exclusive events are calculated, especially since we want those who have either condition but not both.
This choice sums the probabilities of all three groups, which leads to overcounting the residents who have both dementia and a physical disability. This method does not account for the overlap, resulting in an inaccurate probability.
This option correctly uses the inclusion-exclusion principle, adding the probabilities of dementia and physical disability, then subtracting the overlap of those who have both conditions. This provides the accurate probability for residents with either condition, but not both.
This choice incorrectly attempts to find the probability of having at least one condition by taking the complement. The calculation does not focus on the specific requirement of finding the probability of having either condition but not both, leading to a misunderstanding of how to approach the problem.
The accurate probability of a resident having either dementia or a physical disability, but not both, is derived through the inclusion-exclusion principle: adding the probabilities of each condition and subtracting the overlap. This method ensures proper accounting of residents with both conditions, leading to a correct and precise result.
Related Questions
View allAn intravenous drip is infused at a rate of 4.5 milliliters per minute...
The physician has ordered a patient's IV fluid to be increased by 0.15...
If a person is over the age of 80, there is a 20% chance of having hig...
The current reimbursement rate for a specific diagnosis-related group...
Given the following dataset representing hours slept by patients in a...
Related Quizzes
View all0PC1 Planning Instructional Strategies for Meaningful Learning Version 1
AP01 Elementary Literacy Curriculum Version 1
ASO1 Introduction to Statistics for Research Version 1
BJ01 Introduction to Business Finance Version 1
C172 Network and Security Foundations Version 1
C180 Introduction to Psychology Version 1
C180 Introduction to Psychology Version 2
CKC1 Introduction to Humanities Version 1
DZ01 Mathematics for Elementary Educators III MATH 1330 Version 1
FF01 Human Growth and Development Version 1
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations