Marginal probability

Imagine you have ten pieces of candy: five green ones and five red ones. If you pick a candy at random, the probability of it being green is 1/2 (because there are five green candies out of ten total candies).

Now, let's say you want to know the probability of picking a green candy *and* a red candy in two separate rounds of picking. The probability of picking a green candy in the first round is still 1/2, but what about the second round?

Here's where marginal probability comes in. The probability of picking a red candy in the second round *marginalizes* over the first round. In other words, it doesn't matter what happened in the first round when looking at the probability of picking a red candy in the second round.

So, the marginal probability of picking a red candy in the second round is also 1/2. This is because there are still five red candies out of ten total candies, even though some of the candies may have been picked already.

To summarize, marginal probability is the probability of an event occurring, ignoring any prior events or conditions. It allows us to calculate probabilities for multiple rounds or events, without worrying about what happened in previous rounds or events.