What does this mathematical rebus means ?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

I know a nine-letter word having only one vowel.
Do you ?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

A man says, "Brothers and sisters, have I none, but that man's father is my father's son." Who is that man?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

John was driving a bus and got stuck when passing through an underpass. Then came Jacob with a needle and got the bus out of the underpass.

What did the boy do?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?