Final answer:
The question involves principles of probability, particularly the memoryless property and the product rule. While Richard J. Saykally's exact derivation is not recounted, the concept is that future probabilities in certain distributions are independent of past events, and independent events' probabilities are multiplied to find the joint probability.
Step-by-step explanation:
The question pertains to the derivation of the expression for the probability of the existence of a particular x-mer in a 1936 paper by Richard J. Saykally. While the details of Saykally's paper and derivation are not provided, the concept can be explained using principles of probability. Saykally's work possibly relates to the memoryless property of certain probability distributions, which states that the future probability distribution of events is not dependent on the past occurrences given the present.
The memoryless property is formalized in the expression P(X > x + k|X > x) = P(X > k). This represents that the probability of a random variable, X, being greater than a certain value x+k, given that it is already greater than x, is the same as the probability of X being greater than k on its own.
The product rule of probability is another key aspect, stating that the probability of two independent events occurring simultaneously can be computed by multiplying their individual probabilities. For example, rolling a die and flipping a coin are independent events, and the overall probability is the product of the probabilities of each separate event.