How do you use a tree diagram to solve combined event problems?

You use a tree diagram to solve combined event problems by mapping out all possible outcomes step-by-step.

A tree diagram is a visual tool that helps you systematically list all possible outcomes of combined events. To create one, start by drawing a branch for each possible outcome of the first event. From the end of each branch, draw additional branches for the possible outcomes of the second event, and so on. This way, you can clearly see all the possible combinations of outcomes.

For example, if you are flipping a coin and then rolling a die, you would start with two branches for the coin flip: one for heads and one for tails. From each of these branches, you would then draw six more branches to represent the six possible outcomes of the die roll (1, 2, 3, 4, 5, and 6). This results in a total of 12 branches, each representing a unique outcome of the combined events.

Each path through the tree diagram represents a different sequence of outcomes. By following these paths, you can easily count the total number of possible outcomes and analyse the probability of specific events. For instance, if you want to find the probability of flipping heads and rolling a 3, you can see that there is one favourable outcome out of the 12 possible outcomes, giving you a probability of 1/12.

Tree diagrams are particularly useful for visualising and solving problems involving independent events, where the outcome of one event does not affect the outcome of another. They help break down complex problems into manageable parts, making it easier to understand and solve them.