Paradox Schmaradox
Warning: Spoiler below. Tem42 has pointed out, quite rightly, that it is more fun to figure out the paradox on your own, so try that first, if you're so inclined.

Principle 2 is your problem, here. (Referring to Tem42's above node.)

Suppose proposition p is 70% likely to be true, and proposition q is also 70% likely to be true. Each proposition, taken individually, is more likely to be true than not.

Now, imagine that you are walking to work, and since it rained last night, the road is a bit muddy. Suppose p represents whether or not you will make it to work without getting mud on your suit. And q represents whether or not a car will run through a puddle, splashing and soaking your suit.

Now, according to this Principle 2, one might assume, "Since it is probable that I will reach my workplace without getting mud on my suit, and since it is probable that I will get there without getting my suit wet, I can conclude that I will probably make it to work with a clean suit."

Of course, the probability that p AND q are true is not 70%, but the probabilities multiplied, or 49%. So, you will probably arrive at work with a wet or muddy suit, and should probably consider an alternate route.

So, even if it is 99.999% certain that an individual lottery ticket will lose, it is only ~99.998% certain that two tickets will both lose, and only ~99.997% certain that all of three tickets will lose, and so forth, with decreasing probabilities that all of an increasingly larger set of tickets will lose.

By the time you reach the 100,000th ticket, the probability that all will lose is some infinitesimal fraction very close to zero, which represents the probability that a large meteor will destroy the earth before the lottery is drawn.