Probability

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Is the regularity shown in this encoded message noise or structure?