Possibilities Versus Probabilities in Statistics

Posted on the 26 March 2014 by Calvinthedog

Sean writes:

Sorry to be another straight male to bombard you with questions, but this is undoubtedly not a story you have heard by now. I had unprotected, vaginal sex with a girl who was 5 months pregnant and had ovarian cancer. I did not use a condom because my idiotic thinking told me – “Can’t get her pregnant twice, right?”. I know nothing of the man who got her pregnant, and I kinda started to freak out. Assuming she is not lying, which I truly believe she is not, she was tested for STD’s by her doctor 1 month ago, and came back clean on everything.

So, I know I’m probably just freaking out here – but what are the chances that after 4 months she did not begin to produce the HIV antibodies, came back with a false negative test, and then passed it to me after 1 time of unprotected vaginal sex? There seems to be some doctors and scientists who believe that you can provide a false negative test after 3 months even, and being on anti-cancer meds could aid in it, seeing as how the persons immune system may already be suppressed. It’s probably about the same as getting struck by lightning twice, eh?

Statistically, anything is possible. She could have given it to you from one vaginal sex episode. She may have HIV although I really doubt it. She could possibly have HIV even with a 4 month negative test. However, statistics is an odds game, and as such, I am willing to bet with 100% certainty that you do not have HIV. You simply did not get it from this woman.

But what is preventing you from getting your own HIV test?

This is the thing about statistics. In statistics, anything is possible. However, once likelihood of a certain result starts getting extremely low we usually just say that that result simply did not occur. Why? Probability. Possibility is one thing and probability is another. In the case above, of course, there is a slight possibility that he got HIV from this woman. But what is the probability that he got it? I place it at basically zero.