Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the black cards is at le...
Find the smallest prime number N such that the following is true: The largest prime factor of N−1 is A; The largest prime factor of A−1 is B; The largest prime factor of B−1 is 7.
9 fair coins are independently tossed in a row. Let X be the random variable denoting the number of instances in which a Head is immediately followed by a Tail during these 9 tosses. The variance of X has the form a/b, where a and b are coprime integers. What is the value of a...