What are the odds of flipping a coin and getting heads five times in a row?
Having flipped a coin four times in a row and got heads every time what are the odds of getting heads again if I flip it one more time?
I don't think probability works in the way you imply.
On the contrary, it works exactly like the way I stated because there is no one right way to ask statistical questions.
Both questions are legitimate statistical questions. The issue then becomes which question is the best fit for the facts at hand. Given the fact that we do not even know if ACARs failed at all, asking the question "what are the odds of the transponder failing given an ACARs failure" is asking a question based upon a false premise.
The
meaningful question in the absence of data is "what are the odds of getting five heads in a row?" or in this case the question I asked about both failing in a short time span. This allows the investigator to compare two or more chains of causation without assuming anything. The alternative is to confuse selection bias with statistical probabilities.