Join Eddie Davila for an in-depth discussion in this video Multiplication rule, part of Statistics Foundations: Probability.
- Earlier we saw the addition rule of probability. Now let's look at the multiplication rule of probability. Let's look at two different scenarios, each with multiple events. Let's say we have a pair of dice. One is red in color. The other is white. If we roll each die, what's the probability both dice will come up with a one? First, let's recognize that these are two independent events. The outcome of rolling the red die in no way influences the outcome of the white die. For two independent events, we find the probability of each individual desired outcome. The odds of rolling a one on the red die is one in six, a 16.7% probability. The odds of rolling a one on the white die is also one in six, also a 16.7% probability. The multiplication rule tells us that to find the probability that both the white and red die come up one, we multiply the probabilities of each individual outcome. 16.7% X 16.7% is 2.79%. There's a 2.79% chance both dice will come up ones. Let's now look at something a little bit different. Let's look at two dependent events. Suppose there are 10 cards face down on a desk. Three of the cards have an X on them. What's the probability you will pick two cards and both cards will have an X on them? Again, we will multiply the probability for each of the two cards picked, but we need to realize that the card picked first removes a card from the table. So, the probabilities for the second card will change. We want two X's, so the odds of picking an X with your first card picked is three in 10, 30%. Now, if we pick an X with card number one, we need to realize that only two of the X cards remain and that in total, only nine cards are left on the table. So, the odds of picking an X with your second pick, provided you picked an X with your first card, is two in nine, 22%. The multiplication rule tells us to multiply these two probabilities, 30% for pick number one, times 22% for pick number two. There is a 6.6% chance you will pick an X card with both of your picks. As you work with multiple event probabilities, first, figure out if you are looking at dependent or independent events. And then, remember that the multiplication rule will not fail you.
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.