Monday, August 8, 2011

Probability Limit

At a Science Café talk about mammals tonight, I heard this statement: "even if the chance of it happening is one in one-million in a given year, the likelihood is high given a span of one-million years." Is that really true? What about in the general case of "if the chance of an event happening is 1 in n, what's the likelihood that the event will occur at least once for n number of trials?"

The expression for that probability is 1 minus the chance that the event will not occur at all during the n number of trials. The chance of the event not occurring each time is (n-1)/n. Raise that to the n-th power for the number of iterations, and subtract from 1, which represents certainty, and the probability that the event happens at least once is:
We wish to find the limit as n approaches infinity. Working out the L'Hopital's rule by hand can be somewhat cumbersome with the exponential term, but with the help of Mathematica, we determine the limit to be:
The answer approximates to = 0.632120559. As n increases, the output probability decreases. However, n only needs to be greater than 485 for the output probability to match the first 3 decimal places after rounding. Of course for any given probability, as the number of trials increase indefinitely, the overall probability of the event occurring at least once approaches certainty. But in the special circumstance here, where the number of trials (n) match the inverse of the probability of each event (1/n), the overall probability approaches (e-1)/e.

Friday, August 5, 2011

Financial Woes of USPS

There is absolutely no doubt that postal offices around the world are struggling, and the United States is no exception. Today, the United States Postal Service (USPS) announced that it is facing $3.1 billion quarterly loss, after posing 2.6% decrease in volume from a year ago. Given these figures, it may not be able to make its $5.5 billion retirement payment in September, and default may be an inevitable possibility.

An independent agency of the United States government, USPS does not receive taxpayer funding. As deficits pile up, the USPS has tried implementing various ways to increase revenue and cut costs. How USPS handles its money has been attention of much criticism. The union enjoys no-layoff contracts, and USPS spends 80% of its budget on salaries and benefits, compared to its competitors' 61% for UPS and 43% for FedEx. Compared to other federal workers, postal employees also pay a smaller portion of their salary for health care. Yet, money management may not be the root cause of financial troubles USPS faces.

Demand is simply falling. Principles of economics indicate that fall in demand corresponds to decrease in quantity of service offered. As people continue to rely on electronic services for communication and transactions, the demand for postal services fall, as shown by the 20% decrease in volume handled from 2006 to 2010. Furthermore, outlook is dismal for USPS, because it mainly relies on first-class mail for its revenue. As business switch to electronic method to cut costs, USPS has to rely on changing consumer behaviors to keep its basis of revenue; there is a "marketing officer tasked with lobbying banks not to switch to electronic statements."

The public and the USPS have considered cutting costs by reducing service. However, the current reputation of USPS is dependent on its quick and cheap delivery for first-class mail. By cutting costs and services, USPS may significantly damage its value. This was inadvertently demonstrated by a recent strike by Canada Post. Demanding better compensation, Canada Post shut down service for 3 weeks. While some businesses were hurt, observers noted that "by going on strike, postal workers have likely sealed their own fate by proving it's possible to function without daily mail delivery."

The fundamental cause of financial problems for USPS is the reduction in demand. Demand for cassette players plummeted drastically over the recent years with development in electronic music players. However, USPS is not like typewriter. Businesses still rely heavily on first-class mailing to advertise, and mailing is the only way to send an original document intact. USPS is the only service that delivers first-class mails, and the colloquially termed junk mail; UPS and FedEx are more involved with package delivery. Mail volume may be down, but USPS still handled an enormous volume of 40 billion items during the third quarter. It's impractical to call for the disband of the first-class mail carrier. Rather, USPS needs to expand its evaluation of alternative methods, from moderately decreasing services to incorporating distance-based fares. Furthermore, regulations regarding the service, authority and regulation over delivery systems should also be closely analyzed. Until then, USPS and the nation may be stuck in this deadlock, as over half million employees and the rest of the nation watch the latest figures dismally.

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