A single number has been drawn from an urn which contains a thousand of them. A witness to this drawing announces that number 79 is drawn; one asks the probability of drawing this number. Let us suppose that experience has made known that this witness deceives one time in ten, so that the probability of his testimony is 1/10. Here the event observed is the witness attesting that number 79 is drawn. This event may result from the two following hypotheses, namely: that the witness utters the truth or that he deceives. Following the principle that has been expounded on the probability of causes drawn from events observed it is necessary first to determine _à priori_ the probability of the event in each hypothesis. In the first, the probability that the witness will announce number 79 is the probability itself of the drawing of this number, that is to say, 1/1000. It is necessary to multiply it by the probability 6/10 of the veracity of the witness; one will have then 9/10000 for the probability of the event observed in this hypothesis. If the witness deceives, number 79 is not drawn, and the probability of this case is 999/1000. But to announce the drawing of this number the witness has to choose it among the 999 numbers not drawn; and as he is supposed to have no motive of preference for the ones rather than the others, the probability that he will choose number 79 is 1/999; multiplying, then, this probability by the preceding one, we shall have 1/1000 for the probability that the witness will announce number 79 in the second hypothesis. It is necessary again to multiply this probability by 1/10 of the hypothesis itself, which gives 1/10000 for the probability of the event relative to this hypothesis. Now if we form a fraction whose numerator is the probability relative to the first hypothesis, and whose denominator is the sum of the probabilities relative to the two hypotheses, we shall have, by the sixth principle, the probability of the first hypothesis, and this probability will be 9/10; that is to say, the veracity itself of the witness. This is likewise the probability of the drawing of number 79. The probability of the falsehood of the witness and of the failure of drawing this number is 1/10.