What is Conditional Probability?
Conditional probability is a mathematical concept that describes the likelihood of an event happening given that another event has already occurred or is assumed to be true It is a type of probability that takes into account the information that is known about the scenario that is being evaluated, allowing for a more granular evaluation of the likelihood of success given the known information.
For example, if a coin is tossed, the probability of flipping a heads is 50%. However, if we assume the coin has already been flipped and it resulted in a “tails,” then the probability of flipping a heads on the next flip is also 50%. This is because the probability of heads and tails remain the same regardless of what has already happened.
But if we were to phrase the questions differently, and ask what is the probability of the coin flipping two heads in a row, then the conditional probability would come into play. Under this scenario, the probability of two heads in a row would be 25%. This is because the probability of getting heads has already been reduced by half due to the fact that a tails has already been flipped.
Five Examples of Conditional Probability
1. Weather Forecast: A weather forecast is a classic example of how conditional probability can help estimate the likelihood of an event happening. For example, a meteorologist can look at today’s weather and determine, with a certain amount of accuracy, what the weather will be tomorrow. By looking at the current temperature, humidity, and other factors, the meteorologist can estimate the probability of rain tomorrow and other meteorological events, given the current conditions.
2. Insurance Analysis: Insurance companies use conditional probability to analyze risk and determine insurance premiums. By looking at a person’s age, gender, driving record, and other factors, the insurance company can estimate the probability of the person filing a claim and use that to determine their premium.
3. Disease Diagnosis: Doctors can use conditional probability to diagnose diseases, based on the patient’s symptoms. By looking at the patient’s symptoms, the doctor can estimate the probability of the patient having a certain disease, and either order additional tests or begin treatment.
4. Stock Market Predictions: Financial analysts use conditional probability to forecast stock market trends. By looking at past performance and other factors, the analyst can estimate the probability of certain stocks increasing or decreasing in value. This can then be used to make educated investment decisions.
5. Lottery Odds: Lottery players can use conditional probability to determine the likelihood of their winning. By looking at the number of possible combinations, the player can estimate the probability of their chosen numbers being selected, and hence their chances of winning the lottery.