There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

If an electric train is travelling south, then which way is the smoke going?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

It is raining today at 11:59 am. What is the probability of sunny weather after 72 hours?

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

What occurs twice in a week, once in a year but never in a day?

I can sizzle like bacon,
I am made with an egg,
I have plenty of backbone, but lack a good leg,
I peel layers like onions, but still remain whole,
I can be long, like a flagpole, yet fit in a hole.

What does this mathematical rebus means ?