Raikov's theorem is a fancy math rule that helps us understand something called probability. Probability is just a fancy word that tells us how likely something is to happen. For example, if you flip a coin, there is a 50% chance it will come up heads.
Now, Raikov's theorem tells us that if we have a big group of things that all have some special qualities in common, then we can use that information to guess about new things that are added to the group. For example, if we have a big group of apples that are all red and round, then if we see a new apple that is red and round, we can guess that it's probably part of the group too.
Raikov's theorem is really helpful for mathematicians who want to make predictions about things, like predicting how a new medicine might work based on how it's worked in the past. So, we can use Raikov's theorem to make smart guesses about things and make less mistakes.