# Tree Diagram and Probabilities

So there are tons of ways to conduct probability problems. One such way is through a Tree Diagram. This is great for children who don’t do well just thinking it out and need a visual representation. So here’s a problem using a dilemma many people have, such as how many boys or girls they would have probability wise.

So here’s a problem. A woman wants to know the odds of her having all girls if she has 3 children so we are going to make a tree diagram.

What is the probability that they will only have boys?

So first off the outcome of a boy or a girl is always 1/2. So the combinations are as follows:

MMM = 1/2 X 1/2 X 1/2 = 1/8, MMF = 1/2 X 1/2 X 1/2 = 1/8, MFF = 1/2 X 1/2 X 1/2 = 1/8

MFM = 1/2 X 1/2 X 1/2 = 1/8 FFF = 1/2 X 1/2 X 1/2 = 1/8 = 1/2, FMF = 1/2 X 1/2 X 1/2 = 1/8

FMM = 1/2 X 1/2 X 1/2 = 1/8

So the probability of getting at least 2 males is:

1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 1/2

So this is a basic way of showing probability. Theres lots of different outcomes. Another example is the probability of getting all males is 1/8 since there are 8 outcomes.

The best part is no matter what this is an example of a theoretical probability. If you would like to see more examples of tree diagrams click here