Welcome to this deck on basic probability trees. Tree diagrams are a great way to visualise the outcomes of several events happening one after another. We'll learn how to use them for independent events, where the outcome of one event doesn't affect the next. You'll learn the two key rules: how to multiply probabilities along the branches, and how to add probabilities for different outcomes.

First, let's be clear on what 'independent events' are. They are events where the result of one has absolutely no impact on the result of the other. A classic example is flipping a coin. Getting a head on the first flip doesn't make you any more or less likely to get a head on the second flip. The events are independent.

A probability tree starts at a point, and then branches out to show the possible outcomes of the first event. For a coin flip, there would be two branches: one for heads, and one for tails. On each branch, we write the probability of that outcome. For a fair coin, both probabilities would be one half.

A key rule for any set of branches coming from a single point on a probability tree is that the probabilities must always add up to one. This represents all possible outcomes for that stage of the event.