How do you use a tree diagram to find the probability of dependent events?

To use a tree diagram for dependent events, multiply probabilities along branches and adjust for changing conditions.

A tree diagram is a visual tool that helps you map out all possible outcomes of a sequence of events, especially when those events are dependent on each other. Dependent events are those where the outcome of one event affects the probability of the next event.

Start by drawing a branch for each possible outcome of the first event. Write the probability of each outcome along its branch. For example, if you are drawing a card from a deck, the probability of drawing an Ace is 4/52, and the probability of not drawing an Ace is 48/52.

Next, from each of these branches, draw branches for the possible outcomes of the second event. However, because the events are dependent, you need to adjust the probabilities based on the outcome of the first event. For instance, if you drew an Ace first, there are now only 51 cards left, and only 3 of them are Aces. So, the probability of drawing another Ace would be 3/51.

Continue this process for any subsequent events, always adjusting the probabilities to reflect the outcomes of the previous events. To find the probability of a specific sequence of events, multiply the probabilities along the branches of that sequence. For example, the probability of drawing two Aces in a row would be (4/52) * (3/51).

By using a tree diagram, you can clearly see how the probabilities change with each event and calculate the overall probability of a sequence of dependent events.