Assuming a fair coin, the chance of flipping 20 consecutive heads (or tails) isnot1:1,000,000.

Your thinking is faulty. Why on earth would the probability change fromtoP/20? Each coin flip is an independent event, which means a coin flip does not depend on the outcome of any prior flips. What you’re implying is that the probability of a single head is 1/4 because you have to get it on a specific flip. So no, your answer to the first question is not correct.P

For the second question, consider each morning’s 20 flips as a single daily event (for example, you could have a machine that flips 20 separate coins simultaneously). The probability of success on any morning is, say. Consequently, the probability of failure on any given morning is 1 –P. What is the probability ofPconsecutive failures, bearing in mind that each morning’s flip result is an independent outcome? And once you know the probability ofnconsecutive failures, you should know how to calculate the probability of at least one success (because “at least one success” is equivalent to “notnconsecutive failures”).n