Explain in detail and give an original example of the four types of probability.
1) Marginal probability
2) Union probability
3) Joint probability
4) Conditional probability
All of these involve probabilities of two (or more) variables or events. The two variables (let's call them x and y) can be independent or not.
1) Marginal probability P(x)
This is the probability of x, over all possible y's. If x is some event, you would find it by dividing the number of times x occurred by the total number of observations. You wouldn't consider what y did during that same time.
2) Union probability P(x or y)
This is the probability that either x or y or both will occur. If x and y are events A and B, then the union probability is the sum of the two events minus the joint probability:
P(A or B) = P(A) + ...