Let us consider now the probability of the totality of several testimonies upon an established fact. In order to fix our ideas let us suppose that the fact be the drawing of a number from an urn which contains a hundred of them, and of which one single number has been drawn. Two witnesses of this drawing announce that number 2 has been drawn, and one asks for the resultant probability of the totality of these testimonies. One may form these two hypotheses: the witnesses speak the truth; the witnesses deceive. In the first hypothesis the number 2 is drawn and the probability of this event is 1/100. It is necessary to multiply it by the product of the veracities of the witnesses, veracities which we will suppose to be 9/10 and 7/10: one will have then 63/10000 for the probability of the event observed in this hypothesis. In the second, the number 2 is not drawn and the probability of this event is 99/100. But the agreement of the witnesses requires then that in seeking to deceive they both choose the number 2 from the 99 numbers not drawn: the probability of this choice if the witnesses do not have a secret agreement is the product of the fraction 1/99 by itself; it becomes necessary then to multiply these two probabilities together, and by the product of the probabilities 1/10 and 3/10 that the witnesses deceive; one will have thus 1/330000 for the probability of the event observed in the second hypothesis. Now one will have the probability of the fact attested or of the drawing of number 2 in dividing the probability relative to the first hypothesis by the sum of the probabilities relative to the two hypotheses; this probability will be then 2079/2080, and the probability of the failure to draw this number and of the falsehood of the witnesses will be 1/2080. If the urn should contain only the numbers 1 and 2 one would find in the same manner 21/22 for the probability of the drawing of number 2, and consequently 1/22 for the probability of the falsehood of the witnesses, a probability at least ninety-four times larger than the preceding one. One sees by this how much the probability of the falsehood of the witnesses diminishes when the fact which they attest is less probable in itself. Indeed one conceives that then the accord of the witnesses, when they deceive, becomes more difficult, at least when they do not have a secret agreement, which we do not suppose here at all. In the preceding case where the urn contained only two numbers the _à priori_ probability of the fact attested is ½, the resultant probability of the testimonies is the product of the veracities of the witnesses divided by this product added to that of the respective probabilities of their falsehood.