Martin Gardner's two-children paradox posits two scenarios, in one we know that of children is a girl, and the other older girl. The chances child being girl not same these first 1 3 while second they are 2. Gardner himself believed problem this lies ambiguous way scenarios articulated. However, it possible to show original version provides sufficient content for meaningful explanation unexpect...

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill-posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill-posed problem show...

The classical interpretation of probability together with the Principle of Indifference are formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called Labeling Irrelevance is defined in the category of Haar probability spaces, it is shown that Labeling Irrelevance is violated and Bertrand’s Paradox is interpreted as the very proof of...

This paper analyzes a simple, repeated game of simultaneous entry and pricing. We report a surprising property of the symmetric equilibrium solution: If the number of potential competitors is increased above two, the market breaks down with higher probability, and the competitive outcome becomes less likely. More potential competition lowers welfare – another Bertrand paradox. The model can als...

Job Search with Bidder Memories This paper revisits the no-recall assumption in job search models with take-it-or-leave-it offers. Workers who can recall previously encountered potential employers in order to engage them in Bertrand bidding have a distinct advantage over workers without such attachments. Firms account for this difference when hiring a worker. When a worker first meets a firm, t...

The classical interpretation of probability together with the Principle of Indifference are formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called Labeling Invariance is defined in the category of Haar probability spaces, it is shown that Labeling Invariance is violated and Bertrand’s Paradox is interpreted as the very proof of v...

This paper discusses conditional probability P( A | B), or the probability of A given B. When P(B) > 0, the ratio formula determines P( A | B). When P(B) = 0, the ratio formula breaks down. The Borel-Kolmogorov paradox suggests that conditional probabilities in such cases are indeterminate or ill-posed. To analyze the paradox, I explore the relation between probability and intensionality. I arg...

one of the most practical routine tests for convergence of a positive series makes use of the ratio test. if this test fails, we can use rabbe's test. when rabbe's test fails the next sharper criteria which may sometimes be used is the bertrand's test. if this test fails, we can use a generalization of bertrand's test and such tests can be continued innitely. for simplicity...

Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency de nition of probability; yet they may appear well posed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a de n...