A tale of two probabilities

Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.     

从“不爱红妆爱武妆”的英译谈英语中的Antimetabole结构

Antimetabole是英语中一种运用得很广泛的辞格.许渊冲教授新译<毛译东诗词选>中<为女民兵题照>"不爱红装爱武装"的英译达到了绘声绘色的翻译效果.通过了解antimetabole的定义、特点和修辞功能,以及antimetabole与Chiassmus,palindrome和anadiplosis之间的相互比较,我们的文学鉴赏和写作水平可以得以进一步提高.     

Children’s concept of probability as inferred from their binary choices—revisited

Children had to choose one of two urns—each comprising beads of winning and losing colours—from which to draw a winning bead. Three experiments, aimed at diagnosing rules of choice and designed without confounding possible rules with each other, were conducted. The level of arithmetic difficulty of the trials was controlled so as not to distort the effects of the constituent variables of proportion. Children aged 4 to 11 first chose by more winning elements and proceeded with age to choices by greater proportion of winning elements. There were some indications of intermediate choices by fewer losing elements and by greater difference between the two colours. Distinguishing correct choices from favourable draws, namely acknowledging the role of chance in producing the outcome and insisting on the right choice, grew with age. Children switched rather early from considering one dimension to two; they combined the quantities of winning and losing elements either additively by difference or, with age, mostly multiplicatively by proportion. Guided playful activities for young children, based on this research, are suggested for fostering acquisition of the basic constituents of the probability concept: uncertainty of outcome, quantification by proportion, and the reverse relation between the chances of complementary events.     

Weighted Means Through the Looking Glass

Each weighted mean of two values has a counterpart, equidistant from the arithmetic mean, obtained by exchanging roles between the weights or by inversing each weight. These elementary relations are apt for introductory courses.     

An Inside Look at the Two Envelopes Paradox

When two sealed envelopes contain money, one twice as much as the other, a player should be indifferent between them. But when one envelope is opened, one's decision should vary as a function of the observed value and one's subjective probabilities.     

The Unrelenting Exchange Paradox

An elusive probability paradox is analysed. The fallacy is traced back to improper use of a symbol that denotes at the same time a random variable and two different values that it may assume.     

Lewis Carroll’s Obtuse Problem

Carroll’s apparently impeccable solution to one of his probability problems is shown to answer another problem that is based on reasonable assumptions. His original assumptions, however, are self contradictory, hence entailing paradoxical results.     

A Classic Probability Puzzle

A classic probability puzzle, presenting an absurd result, is analysed. Clearing the confusion caused by this problem sheds light on basic concepts of probability theory.