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Two good starting points are here: Allen, Helen, and Mark Taylor. “The Use of Technical Analysis in the Foreign Exchange Market.” The Journal of International Money and Finance, June 1992, pp. 304-314. Lui, Y.H., and D. Mole. “The Use of Fundamental and Technical Analyses by Foreign Exchange Dealers: Hong Kong Evidence.” The Journal of International Money ...

Let's approach the answer to your question from a pure trading and risk management perspective because looking at it from a mathematical standpoint nor quant standpoint does not yield you much here: 1) Bollinger bands are nothing else than standard deviation envelopes around the mean of past prices of the underlying. So, as far as simple probabilities go, ...