Mathematical principles of probability entail that for any future event, the probability that it will occur is at least as great as the probability that both it and some other given event will occur. Consider, for example, the following statements that were shown to subjects in a 1998 study.
X. The percentage of adolescent smokers in Texas will decrease at least 15% from current levels by September 1,1999.
Y. The cigarette tax in Texas will increase by $1.00 per pack in 1999.
Z. The cigarette tax in Texas will increase by $1.00 per pack in 1999 and the percentage of adolescent smokers in Texas will decrease at least 15% from current levels by September 1,1999.
Z ("Y and X") could not have been more probable than X. Nevertheless, many of the subjects judged Z to be more probable than X. This mistaken form of reasoning, displayed with surprising frequency in various studies in addition to the 1998 study, is known as the "conjunction fallacy".
A number of researchers have offered alternative explanations for the seeming manifestations of the mistake, thus arguing that the fallacy is less widely committed than the various studies would indicate. Some have claimed that research subjects can take "probability" in a sense that does not conform to the mathematical principles of probability. Detailed descriptions of some such conceptions of "probability" have been developed under the names of "confirmation" and "support." Other researchers would claim, correctly, that subjects shown Z("Y and X") and X simultaneously will sometimes think of X as involving the negation of Y - as a claim that the percentage of adolescent smokers in Texas will decrease, but without the $1.00 increase in the cigarette tax.
However, although the subjects in the 1998 study were to consider X and Z simultaneously, the statements were presented in terms of bets rather than explicit requests for judgments of relative probability. Subjects were asked to choose between Z and X, with a chance of winning $50.00 if the chosen statement turned out to be true. Terms such as "most probable", "likely", etc., were thus avoided and the interpretation of X in conjunction with the negation of Y was thereby eliminated. And with these alternative explanations eliminated, many of the subjects nonetheless bet on Z rather than X.
1. The passage most strongly indicates that the author would agree with which of the following statements? a) None of the subjects in the various studies other than the 1998 study who seemed to commit the conjunction fallacy actually did commit it.
b) People who have studied the mathematical principles of probability are very unlikely to commit the conjunction fallacy.
c) The conjunction fallacy is rarely committed outside of betting contexts.
d) Many of the subjects in the various studies in addition to the 1998 study probably committed the conjunction fallacy.
e) The conceptions of "probability" that underlie everyday use of the word rarely, if ever, conform to the mathematical principles of probability.
2. If the claims of the passage are correct, then which of the following best explains why the interpretation of X in conjunction with the negation of Y was eliminated as claimed from the highlighted text?a) Most of the subjects of the 1998 study recognized that cigarette taxes tend to decrease adolescent smoking.
b) Most of the subjects of the 1998 study interpreted X so as to also include the additional information of Y (as "X and Y " or "Z").
c) Subjects of the 1998 study preferred winning $50 to winning less amount.
d) Subjects of the 1998 study who bet on X would win $50 only if Y turned out to be true.
e) Subjects of the 1998 study who bet on X could have won the $50 whether or not Y turned out to be false.
3. The final sentence of the passage mentions the elimination of "alternative explanations" of the 1998 study results. The passage most strongly suggests that the author wanted to eliminate the explanations in order toa) support the claim that the concept of probability is usually interpreted so as not to conform to the mathematical principles of probability
b) counter the claim that the conjunction fallacy is in fact a mistake of reason
c) support an explanation of why some people commit the conjunction fallacy even when they bet on particular outcomes without making explicit probability judgments
d) counter the claim of some researchers that the conjunction fallacy is less frequently committed than various studies would seem to indicate
e) support the point that the conjunction fallacy was not committed by the subjects in studies prior to the 1998 study
4. The use of bets in the 1998 study was intended to deflect objections that would be based on which of the following issues?a) The possibility of research subjects interpreting "probability" so as not to conform to the mathematical principles, and their interpretation of X to include additional information
b) The possibility of research subjects interpreting "probability" so as not to conform to the mathematical principles, and the lack of motivation of some of the subjects
c) Failure of research subjects to recognize that adolescent smoking could decrease even when the cigarette tax remains the same
d) The interpretation of X by some study subjects to include additional information and their lack of concentration on the assigned tasks
e) The fact that some of the research subjects did not commit the conjunction fallacy