 Even if we reject GJ, it does not follow that we must reject GK, which concerns knowledge closure. Consider the lottery example again. How justified we are in believing that ticket 1 will lose depends on how probable its losing is. Now, the probability that ticket 2 will lose is equal to the probability that ticket 1 will lose. The same goes for each ticket. However, consider the conjunction, Ticket 1 will lose &amp; ticket 2 will lose. The probability of this conjunctive proposition is less than the probability of either of its conjuncts. Suppose we continue to add conjuncts. For example, next in line will be: Ticket 1 will lose &amp; ticket 2 will lose &amp; ticket 3 will lose. Each time a conjunct is added, the probability of the resulting proposition is still lower. This illustrates the fact that we can begin with a collection of propositions each of which surpasses some threshold level of justification (let it be whatever is necessary for a belief to count as “justified” according to GJ) and, by conjoining them, we can end up with a proposition which falls below that threshold level of justification. We may “justifiably believe” each conjunct, but not the conjunction, so GJ fails. However, we need not reject GK on these grounds. Even if we grant that we justifiably believe that Ticket 1 will lose is true we might deny that we know that this proposition is true. We might take the position that if we believe some proposition p on the basis of its probability, nothing less than a probability of 1 will suffice to enable us to know that it is true. In that case GK will not succumb to our objection to GJ, for if the probability of two or more propositions is 1 then the probability of their conjunction is also 1. 