Probability is about the chances or likelihood of something happening in the future.
And Likelihood is about how well the data we have matches a specific outcome or hypothesis.
Probability#
Probability is the long-run frequency of how often something occurs. It exists in one universe, meaning that probabilities are related to each other and must add up to one.
For example, if you flip a fair coin, there’s a 50% probability of getting heads and a 50% probability of getting tails.
It’s often used when we know all the possible outcomes of an event and want to figure out how likely each outcome is.
Likelihood#
Likelihood is used in statistics when we don’t know the probability of something happening.
For example, if you have symptoms like coughing and fever, there’s a high likelihood that you have a cold, based on what we know about the common symptoms of a cold.
It’s commonly used in statistics to measure how probable it is that a certain set of data would occur if a particular hypothesis were true.
Compare/Contrast#
Likelihoods are probabilities of the observed data under different scenarios. They do not add up to one and cannot be interpreted as probabilities.
If you have a fair coin, the probability of zero heads is 1/4, the probability of one head is 1/2, and the probability of two heads is 1/4. These probabilities add up to one.
But if you have an unfair coin, the probabilities will be different. If you flip the situation around and only observe two heads, the likelihood of two heads will depend on which type of coin you flipped.
Conclusion#
In conclusion, probability is used when we know the universe we are in, and likelihood is used when we don’t know the probability of something happening. They are two different ways of looking at the same thing.