Compound EventsReference > Mathematics > Probability
So far we have learned how to calculate the probability of a single event happening, but sometimes life isn't so simple as one event happening by itself; sometimes we're interested in two events happening together, or one after another. Calculating the probability of two events both happening isn't terribly complicated; we just calculate the two individual probabilities, and multiply them together. We do need to pay attention to whether the events are dependent or independent; if the events are dependent, our sample space (possible outcomes) may change, and our number of desired outcomes may change, based on the first event.
If I roll a four-sided die, and a six-sided die, what is the probability that they will both show the number one?
These are independent events. First we calculate the probability of getting a one on the four-sided die. That's
This answer makes a lot of sense, because we could have calculated it a different way:
If you consider the two die rolls as a single event, there are 24 possible outcomes (see our fundamental counting principle page for an explanation), and only one of them is desired.
A jar has 20 red jelly beans and 5 green ones. I pick two jelly beans. What is the probability that they are both green?
To solve this, we treat it as two events. First I pick a jelly bean, then I pick another one. These are dependent events, because the first event affects the second one.
My sock drawer has 5 red socks and 4 blue socks. If I randomly pick two socks, what is the probability that I'll have a pair of blue socks?
First sock: 9 possible, 4 desired. P =