chain rule in statistics
The chain rule in statistics helps us calculate the probability of something happening, based on a series of related events. For example, let's say you wanted to know the probability of getting at least one tail when tossing a coin three times. The chain rule would help you figure out the answer to that.
First, you would take the probability of getting one heads in the first toss (or 1/2, since a coin has a 50-50 chance). Then, you would calculate the probability of getting one heads in the second toss (or also 1/2). Finally, you would calculate the probability of getting one heads in the third toss (again, still 1/2).
The chain rule then says that you multiply all these probabilities together to get the final probability of getting at least one tail when tossing a coin three times. So the answer would be (1/2) x (1/2) x (1/2) = 1/8. That means that the probability of getting at least one tail when tossing a coin three times is 1 in 8.
First, you would take the probability of getting one heads in the first toss (or 1/2, since a coin has a 50-50 chance). Then, you would calculate the probability of getting one heads in the second toss (or also 1/2). Finally, you would calculate the probability of getting one heads in the third toss (again, still 1/2).
The chain rule then says that you multiply all these probabilities together to get the final probability of getting at least one tail when tossing a coin three times. So the answer would be (1/2) x (1/2) x (1/2) = 1/8. That means that the probability of getting at least one tail when tossing a coin three times is 1 in 8.