Data Management general question

Question

hello,

I have an inquiry regarding a concept in data management, which is to explain why odds can be greater than one but probabilities must be between 0 and 1?

would appreciate any help.

Answer 1

Hi Rahman

Odds and probability are from two different concepts. Probability comes from statistics, and odds come from gambling.

Probability is calculated by dividing the desired outcome by all possible outcomes. Since the denominator of that fraction is "all possible outcomes" , the fraction can't be greater than one, since a probability of one implies that the desired outcome is indeed all possible outcomes. Likewise, if the desired outcome is none of the possible outcomes, then the probability must be zero. Thus, probability by definition must lie between zero and one.

Odds, on the other hand, try to to measure the value of a given outcome, given it's probability. This is the basis for gambling - I bet on an outcome with X probability and you pay me Y if I'm right. If I'm wrong, you keep my bet.

True odds are set by dividing the probability of being wrong, by the probability of being right. So, in a game where the probability of being right is, say, 1/4 or 0.25, the probability of being wrong is 0.75/0.25 or 3. We usually state that as 3:1 or 3 to 1. Events like horse racing do not have a way of predicting the exact probability that a horse will win, so the track gods add up the money bet on each horse and divide it by the total amount bet, and use that as the probability of winning, then create the odds in the usual fashion described above.

So, odds will be greater than 1, whenever the probability of success is less than 0.5.

Hope that helps.