Elon Musk's testing tweet is pretty dumb but shows how testing probabilities can be tough. Musk likely was using the BD Veritor antigen test (if I'm wrong please correct me). From their FDA EUA, BD gives the following specificity and sensitivity numbers 1/6

100% specificity means that no one who was healthy got a positive result i.e – there are NO false positives. Caveat, the numbers from the EUA are from a smallish sample so this number has likely gone down a bit over time. 2/6

84% sensitivity means that, if you have the disease, 84% of the time you will get a positive result. But, this also means if you have the disease you will get a negative result 16% of the time 3/6

Elon took four tests and got 2 positive and 2 negative results. Assuming test independence there are 6 ways this could happen (PPNN, NNPP etc) Using 4 choose 2 = 6 we can then calculate the probability of getting this set of results (h/t @soundofcolor for help with the math) 4/6

The chance that Elon would get those results is 10% It's not the most likely outcome but well in the range of possibility! That means that 1 one out of every ten covid positive people who took four tests would get these results. 5/6

This is why these rapid antigen tests are not used for diagnosing but just screening. Elon either knows this and wants to cast doubt on covid/covid testing or needs to take a remedial stats class 6/6