Question 8: The probability of event X happening given event Y happens is p. What is the probability that if Y happens five times, X does not happen at least once?
My question: I said that since the probability x happens is p, then the probability x does not happen is (1-p). Thus the probability that x does not happen 5 times in a row is (1-p)^5. But the solution showed that the answer is 1- p^5 as this represent 1 - P(x happens 5 time). But doesn’t P(x happens 5 times) exclude the probability x happens 4 times, or 3 times or 2 times?