First time poster. I have something of a probability riddle that I'm not sure how probability experts would think about it. The story is as follows:
My spouse and I received a second dose of the pfizer vaccine on Jan 14 and traveled to the USA on Jan 17. Our four children did not receive the vaccine, and no one in the family has any indication of having covid previously. Due to covid restrictions, we were unable to return home (outside of USA) until Feb 23. On Feb 15, my wife and I, with our two older children took antibodies tests; my wife and I had confirmed antibodies from the vaccine, my children did not have antibodies. In order to fly, we all had to take a PCR test within 3 days of flying, which we did at a reputable lab and received negative results. Upon arrival to our home country, we took another PCR test in the airport, which yielded all of the children negative, but my wife and I were positive. My kids retested 2 days later and were all negative again, and my wife and I retested this morning and are awaiting results.
Let's give the following assumptions: they are testing 100,000 people per day, with 4% positive rate. Reports put false positive rates at somewhere between .8% and 3.5%. False negative rates are a little more challenging because of the way the infection develops. A recent study put the overall discordant rate at around 0.05%. We do not know the discordant rates for the antibodies test, but the results were consistent with our expectations based on our vaccine and no known exposure or infection over the course of the the past year?
My question for the group is what is the probability of both my wife and my own positive test after the flight being incorrect, and that whatever results we receive from today's test are correct?
And, to make it fun, would you bet that our test results today would be positive or negative?
My spouse and I received a second dose of the pfizer vaccine on Jan 14 and traveled to the USA on Jan 17. Our four children did not receive the vaccine, and no one in the family has any indication of having covid previously. Due to covid restrictions, we were unable to return home (outside of USA) until Feb 23. On Feb 15, my wife and I, with our two older children took antibodies tests; my wife and I had confirmed antibodies from the vaccine, my children did not have antibodies. In order to fly, we all had to take a PCR test within 3 days of flying, which we did at a reputable lab and received negative results. Upon arrival to our home country, we took another PCR test in the airport, which yielded all of the children negative, but my wife and I were positive. My kids retested 2 days later and were all negative again, and my wife and I retested this morning and are awaiting results.
Let's give the following assumptions: they are testing 100,000 people per day, with 4% positive rate. Reports put false positive rates at somewhere between .8% and 3.5%. False negative rates are a little more challenging because of the way the infection develops. A recent study put the overall discordant rate at around 0.05%. We do not know the discordant rates for the antibodies test, but the results were consistent with our expectations based on our vaccine and no known exposure or infection over the course of the the past year?
My question for the group is what is the probability of both my wife and my own positive test after the flight being incorrect, and that whatever results we receive from today's test are correct?
And, to make it fun, would you bet that our test results today would be positive or negative?