Understanding Probability of HIV and Herpes in Blood Donors

  • Context: Undergrad 
  • Thread starter Thread starter mirandasatterley
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    Probability Terminology
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Discussion Overview

The discussion revolves around the interpretation of statistical data regarding the prevalence of HIV and herpes among blood donors, specifically focusing on the meaning of the union of these two conditions as represented in the data.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions whether the phrase "HIV or herpes" refers to the union of the two conditions.
  • Another participant confirms that "A or B" indicates the union and provides a general formula for calculating probabilities involving unions and intersections.
  • A later reply corrects a numerical error regarding the probability of donors testing positive for both herpes and HIV.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of "HIV or herpes" as the union, but there is a correction regarding the specific probability value for donors testing positive for both conditions.

Contextual Notes

The discussion includes a potential misunderstanding of the probability values and their implications, particularly regarding the intersection of the two conditions.

mirandasatterley
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Data gathered at a particular blood center show that 0.1% of all donors test positive for human immunodeficiency virus (HIV), 1% test positive for herpes, and 1.05% test positive for HIV or herpes.

Does the part in bold mean the union of HIV and herpes?
 
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Yes "A or B" means in set A or in set B and, yes, that is the union. Notice that the value for "HIV or Herpes" is slightly LARGER than for herpes only.
In general, P(A or B)= P(A)+ P(B)- P(A and B). Here, since 1.05= 0.1+ 1- 0.05 we can se that the test is 0.5 positive for "Herpes and HIV".
 
Halls, I know you meant 0.05 positive for "Herpes and HIV".
 
Thanks. Yes, of course, 0.05.
 

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