Three Puzzles about a Math Toy

Recently, my wife bought the following wooden toy from a clearance bin at Target. It's a set of six dials, rainbow-colored, that are connected by a wooden axle.

Photo Credit: eBay

The dials are shaped like decagons, and each side of the dial is painted as follows:

• The red dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• The orange dial: The following mathematical operators, in this order: +, -, x, +, -, x, +, -, x, +. Note that there are consecutive plus signs on the dial.
• The yellow dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• The green dial: The = sign appears on all sides
• The blue dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• The purple dial: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Playing around with this toy, I came up with three puzzles. (Let me know if someone else has published these before!)

1. Randomly (and independently) spin each of the six dials of the toy. Look at the mathematical statement that appears on the top of the toy. What is the probability that the mathematical statement is correct?
2. Spin the dials so that you form ten mathematical statements, one on each of the ten sides of the toy simultaneously. What is the maximum number of correct mathematical statements that you can display at the same time?
3. Randomly (and independently) spin each of the six dials of the toy to form ten mathematical statements, one on each of the ten sides of the toy simultaneously. What is the probability that at least one side of the toy will show a correct equation?

I think I can solve puzzle #1 using the rules of probability and mathematics--if I can organize the sample space effectively. Right now, I can make some deductions about puzzle #2. I think I will need a computer program and some brute force to tackle puzzle #3. Let me know in the comments if you have any ideas on how to address these three puzzles.