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How many test executions are required (and how many must pass) to say my software works with 95% confidence?

I have some software that operates non-deterministically. Running a test on the code can result in a pass or fail depending on unknown external factors. Assuming that the odds of passing or failing are equal because of these factors, how many times must I run the test, and how many times must the software pass the test so that I can say with 95% confidence that the software works as expected?