Since these independent events either occur or do not occur, we can use binomial distribution to determine the theoretical probability of either outcome with a given number of successes or failures (total - successes) or by probability → 1 - success probability = failure probability.
Since the problem is either looking for all or none, we can narrow n! / (n - x)!x! p^x q^n-x down to (probability)^(days). All the rest cancels out.
