Probability and Odds

Suppose you have a 25 percent chance of getting X. How do we convert a probability to odds?

Let p = 25 percent

Odds is: (1-p) to p

Which is (1-0.25) to 0.25

which is 0.75 to 0.25

which is 3 to 1

In other words, a 25 percent probability is the same as 3 to 1 odds.

Now it is important to note whether these are odds in favor or against.

3 to 1 against means that out of 4 turns, 3 will be something you don't want and 1 will be something you do want.

3 to 1 in favor means that out of 4 turns, 3 will be something you do want and 1 will be something you do not want.

Question: If the odds are 9 to 1 against X occuring (sometimes written 9:1) , then what is the probability (percentage) that X will happen?

Answer: 10 percent