Two visitors are arriving at a house at the same time. Current population wide prevalence of infection is 0.01, i.e. 1%
The visitors are arriving from different destinations, and their infection status are independent of each other. No one in the house is infected.
Total probability of having someone infected in the house should be 0.01 + 0.01 = 0.02 given visitors are independent.
However, the probability of both visitors being infected is 0.01 x 0.01 = 0.0001 , again, given they're independent.
Should we use conditional probability here? If so, how? Both calculations apply to the real life situation at hand, so how do we apply fundamental probability calculations to real life here?
Update: In addition to Henry's answer, anybody arriving at this question via google may find the following blog post from scientific American also helpful. The authors are following the same approach Henry is suggesting.