occur in the present case when the witness does not deceive and is not mistaken at all, and when he deceives and is mistaken at the same time. One may form the four following hypotheses:
1st. The first and second witness speak the truth. Then a white ball has at first been drawn from the urn A, and the probability of this event is 12, since the ball drawn at the first draw may have been drawn either from the one or the other urn. Consequently the ball drawn, placed in the urn B, has reappeared at the second draw; the probability of this event is 11000001, the probability of the fact announced is then 12000002. Multiplying it by the product of the probabilities 910 and 910 that the witnesses speak the truth one will have 81200000200 for the probability of the event observed in this first hypothesis.
2d. The first witness speaks the truth and the second does not, whether he deceives and is not mistaken or he does not deceive and is mistaken. Then a white ball has been drawn from the urn A at the first draw, and the probability of this event is 12. Then this ball having been placed in the urn B a black ball has been drawn from it: the probability of such drawing is 10000001000001; one has then 10000002000002 for the probability of the compound event. Multiplying it by the product of the two probabilities 910 and 110 that the first witness speaks the truth and that the second does not, one will have 9000000200000200 the probability for the event observed in the second hypothesis.
3d. The first witness does not speak the truth and the second announces it. Then a black ball has been drawn from the urn B at the first drawing, and after
