Join Eddie Davila for an in-depth discussion in this video Probability trees, part of Statistics Foundations: Probability.
- When you're trying to calculate probabilities for multiple events it's often helpful to draw a probability tree to visualize how the events might occur. Let's use a probability tree to see how probabilities will change as we flip a coin two times. Let's build a probability tree for two successive coin flips. We flip the first coin and it turns up as heads or tails, one branch for each outcome. Each branch has a probability of 50%. Remember we're flipping the coin twice. It doesn't matter what the result was on flip number one. So we flip again. Now next to both the heads outcome from flip number one and the tails outcome, we add two more branches. And again, each branch has a probability of 50%. We can then follow the paths of the four outcomes at the end of our tree. One is heads flip one, heads flip two. Another is heads, then tails. At the bottom of the tree we have tails heads and tails tails. If we multiply the probabilities along each of the four paths we can find the probability of each of our four outcomes. The other great thing about probability trees is that we can measure how probability changes after each outcome. In other words, if the result of flip one is heads we now know the probability of flipping heads on both coins went from 25% before flip number one to 50% now that heads came up the first time. Let's look at a slightly more complex example where the odds are not always even and where there are more than two possible outcomes. Here's a set of health-related data. In a study that followed 1000 people throughout their lives, 20% lived less than 75 years. 50% lived between 75 and 85 years and 30% lived more than 85 years. So for event number one, three branches, one for each outcome. Each branch marked with the related probability. Next we'll build the branches for some exercise related probabilities. First, we have two branches for those that lived less than 75 years. 20% of those that lived less than 75 years exercised at least three days per week. That means 80% did not. We also have two branches for the 75 to 85 group. Among the group that lived 75 to 85 years, 30% exercise at least three days per week, 70 did not. And two more branches for the 85 plus group. Among the group that lived over 85 years 60% exercised at least three days per week and 40% did not. Let's now multiply the probabilities down each path. These give us the probabilities for each of the six outcomes. And since we know 1000 people participated in the study we can multiply each of those six probabilities by 1000. This will tell us how many people fell into each of the six final outcomes. I have to admit I love probability trees. There's so much information in them. Plus they help us understand conditional probability scenarios. Have some fun today, think of some conditional probability scenarios and then create a probability tree of your own. You can thank me later.
Eddie explains that probability is used to make decisions about future outcomes and to understand past outcomes. He covers permutations, combinations, and percentiles, and goes into how to describe and calculate them. Eddie introduces multiple event probabilities and discusses when to add and subtract probabilities. He describes probability trees, Bayes’ Theorem, binomials, and so much more. You can learn to understand your data, prove theories, and save valuable resources—all by understanding the numbers.