Conditional and joint probability

Conditional probability is the probability that x happens, given that y happens. It's one of the key tools for reasoning about uncertainty in probability theory. Let's say we are talking about your winning the lottery, given that it's a sunny day. Maybe you're feeling lucky! How would we write that in a probability statement? It would be the probability of your lottery win, A, given the probability of it being sunny, B, so P(A|B).

Joint probability is the probability of two things happening simultaneously: what is the probability of you winning the lottery and it being a sunny day?