Understanding Probability of HIV and Herpes in Blood Donors

[mirandasatterley]

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?

 

[HallsofIvy]

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".

 

[EnumaElish]

Halls, I know you meant 0.05 positive for "Herpes and HIV".

 

[HallsofIvy]

Thanks. Yes, of course, 0.05.