ELI5: Explain Like I'm 5

Chain rule (probability)

When we want to know the likelihood of two things happening together, we use something called the chain rule.

Let's say we want to know the probability of it raining outside and then someone using an umbrella. We can break this down into two parts: the chance of it raining and the chance of someone using an umbrella if it's raining.

This is like saying, if we have a bag of marbles, what is the chance of picking a red marble and then picking a blue marble? We have to first figure out the chance of picking a red marble and then the chance of picking a blue marble given that we already picked a red one.

We want to find the overall probability of both events happening, which is the product of the probabilities of each event happening separately. So, the chance of it raining AND someone using an umbrella is equal to the chance of it raining multiplied by the chance of someone using an umbrella if it's raining.

So, if the probability of it raining is 0.5 (50%) and the probability of someone using an umbrella if it's raining is 0.8 (80%), then the probability of it raining AND someone using an umbrella is 0.5 x 0.8 = 0.4 (40%).

In short, the chain rule helps us calculate the probability of multiple events happening together by multiplying the individual probabilities of each event.