Question

In the roulette game, what is the probability of an outcome of:

Any odd number
Any green number
Any number that is red or green
Any number that is red and even

Answer 1

Since I don't know how many numbers are on a roulette wheel:

Odd numbers/all numbers

Green numbers/all numbers

(Red and Green numbers)/all numbers

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Red numbers/all numbers times Green numbers)/all numbers

Answer 2

The standard roulette table has 36 numbers from 1 - 36 , half are red, the other half is black.
The American version also has a 0 and 00, usually in green, I believe the non-American version has only one 0.
I will assume 2 zeros.
prob of odd number = 18/38 = 9/19
any green number = 2/38 = 1/19
red or green = (18+2)/38 = 20/38 = 10/19
red AND even :
I had to actually look at and count a typical board.
I was surprised that there were NOT the same red evens as black evens, (also true for the odds)
(I counted 8 even reds and 10 even blacks)

so prob(red and even) = 8/38 = 4/19