Area Models and Tree Diagrams

Both, tree diagrams and area models are visual ways to represent or obtain clear information. a tree diagram is a diagram that is used to determine the number of possible outcomes in a probability situation. area models are also used to see the possible outcomes but in my opinion in a more organized and faster way than tree diagrams. based on the drawings we can find the theoretical probability. any way area models and tree diagrams go together. since each branch have equally likely chances between themselves the outcomes are added to find the probability of each. but when the branches have a different number of outcomes, they are not equally likely between themselves.
for example a problem that you may obtain and that would ask you to do an area model would be something like this. if you have to take a path only one each time, to get to cave a or to cave b the process is something like this; in your first choice you get three options red road, blue road or green road. if you choose red road then you get to more options you can either choose yellow road and get to cave b, or green road that gets you to cave a. if you chose in your first option road blue, then you have three more new options, either blue or green road that will lead you to cave b, or red road that would take you to cave a. and if in your first option you chose green then you go straight to cave a. this is a probability game, and now you have to find the probability of you landing on cave a or cave b.
then to find the probability is when you use the area model. first you dived the area in 3 equal sections, that represent your first options that you had red blue or green. on the first section that is the red road you dived it in two equal sections obtaining 1/6 chances of cave b and 1/6 of cave a. on your second section you divided it in three sections getting two 1/9 for cave b and 1/9 for cave a. and for your last section you just label it 1/3 of the whole are model for cave a. then your final step is to add the fractions from cave a getting 11/18 meaning 61% of chances of landing in cave a. and 7/18 for cave b meaning 39% of chances.
this is just an explanation of how area models work.