Probability is the chance that an event will occur given as a mathematic ratio that states the number of possible events giving one outcome in relation to a total number of similarly possible events in all outcomes. This ratio is often used in gambling to determine the odds, or the degrees of advantage or disadvantage in a competition based on previous results.
After succumbing to rapid aging, caused by the polarized conductor headbands they the Enterprise landing party was forced to wear, Spock hypothesized that there was a possibility that the transporter could be used to restore the landing party to their original ages. Unfortunately, at the time, the odds were against the aged crewmembers 99.7-to-1. (TAS: "The Lorelei Signal")
Later yet that year, Spock determined the probability of approximately 82.5% that one of the members of the Vedala search party, assigned to find the Soul of the Skorr, was an saboteur. (TAS: "The Jihad")
In a tactical projection of possible future Romulan deployments along the Romulan Neutral Zone, Data determined that their ships were deployed to support a policy of confrontation designed to test Federation defenses along the Neutral Zone. With this analysis, he projected a 90% probability that they would continue to pursue this policy. (TNG: "Data's Day")
In 2370, an alien visiting Deep Space 9 named Cos introduced a gambling machine to Martus Mazur that was able to manipulate the laws of probability. Jadzia Dax later discovered this abnormality when she observed that the spin of over 80% of the solar neutrinos in the space station were spinning clockwise, when the given probability was that about 50% of should be spinning clockwise and the other 50% spinning counterclockwise. (DS9: "Rivals")
One skill necessary for a dabo girl was being able to calculate odds in one's head quickly. Leeta confessed this to a masseur in 2373 while receiving his ministrations. (DS9: "Let He Who Is Without Sin...")