The following struck me as counterintuitive when I first encountered them.

First: Consider a randomly selected group of people. What is the probability that two will have the same birthday? Assume 365-day years, and that they need not be the same age. Before calculating, try guessing at the following.

Suppose there are 20 people in the group.
Suppose 25.
Suppose 35.
Suppose 180.

Next: Consider a circle with an inscribed equilateral triangle. What is the probability that a random chord will be longer than a side of the triangle?

Last: Given A > B > C, it is obvious than A > C if we are dealing with real numbers. Suppose that A, B, & C are probabilities and > stands for is more likely than? Is A more likely than C?

It would be nice if you labeled guesses as guesses and provided examples or analyses if you are not guessing.

I will watch the look count and read posts for a day or so before posting analyses of the above.