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Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

Birthday attacks are a class of brute-force techniques used in an attempt to solve a class of cryptographic hash function problems. These methods take advantage of functions ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection (Diaconis and Mosteller 1989). Given a large number ...

Let S be partitioned into r×s disjoint sets E_i and F_j where the general subset is denoted E_i intersection F_j. Then the marginal probability of E_i is ...

If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways.

n events are said to be mutually exclusive if the occurrence of any one of them precludes any of the others. Therefore, for events X_1, ..., X_n, the conditional probability ...

The probability that a variate would assume a value greater than or equal to the observed value strictly by chance: P(z>=z_(observed)).

The portion of the probability distribution which has a P-value equal to the observed P-value.