There can be examples in which each single premise is more likely true than not and yet it would be unreasonable to accept the conjunction of the premises. Professor Henry Kyburg, who was known for his work in probability and logic, clarified that the issue here is one of closure – specifically, closure under conjunction. There are examples where it is reasonable to accept P and reasonable to accept Q without its being reasonable to accept the conjunction (P&Q). Lotteries serve as very intuitive examples of this, because in a basic non-discriminatory finite lottery with only a single winner to be drawn, it is sound to think that ticket 1 is a loser, sound to think that ticket 2 is a loser...all the way up to the final number. However, clearly it is irrational to accept the conjunction of these statements; the conjunction would deny the very terms of the lottery because (taken with the background knowledge) it would entail that there is no winner.