From the observation that each member of a group could possess a characteristic, it is fallacious to conclude immediately that it is possible for all the group’s members to possess the characteristic. An example in which the fallacy is obvious: arguing that because each of the players entering a tennis tournament has a possibility of winning it, there is therefore a possibility that all will win the tournament.

Which one of the following commits the fallacy described above?

(A) You can fool some of the people all of the time and all of the people some of the time, but you cannot fool all of the people all of the time.

(B) Each of the candidates for mayor appears at first glance to possess the necessary qualifications. It would therefore be a mistake to rule out any of them without more careful examination.

(C) Each of the many nominees could be appointed to any one of the three openings on the committee. Therefore it is possible for all of the nominees to be appointed to the openings on the committee.

(D) If a fair coin is tossed five times, then on each toss the chance of heads being the result is half. Therefore the chance of heads being the result on all five tosses is also half.

(E) It is estimated that ten million planets capable of supporting life exist in our galaxy. Thus to rule out the possibility of life on worlds other than Earth, ten million planetary explorations would be needed.

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