In this video, we'll explore an introduction to probability our learning objectives are to describe the concept of probability and use the rules of probability to perform basic probability calculations. First, we'll look at some definitions. Probability is the chance that an event will or will not occur. The terms are typically expressed in fractions or decimals. An event is one or more of the possible outcomes of a situation or experiment, and an experiment is an activity which produces an event. The sample space is a set of all possible outcomes from an experiment. A couple more terms that are important include the term mutually exclusive, events are termed mutually exclusive when one and only one can take place at the same time, for example, if you flip a coin, you can only get heads or tails, but you can't get heads and tails at the same time. Collectively exhaustive refers to lists containing all of the possible events, which may result from an experiment. Now, the classical calculation for probability is the probability of an event P and it's equal to the number of outcomes where the event occurs N, divided by S, the total number of possible outcomes, and where each of the possible outcomes are equally likely. Let's look at the rules and conditions of probability. There are typical conditions of concern. One is the case where one event or another will occur or the situation with two or more events where both may occur at the same time or in succession. In the first case, we have marginal or what we call unconditional probability, let's say there is some event A that occurs and we'll call this P of A or the P of an event A occurring. It's a single probability, and when a single probability is involved, only one event can take place. Let's look at an example, let's say we have a production lot of 100 parts, and in that production lot of 100 parts, we have one defective parts. What is the P or probability of selecting one part randomly from the lot and drawing the defective? To perform this calculation, the probability of drawing one defective is 1 out of 100 or 0.001, we could also make this a percentage multiplied by 100 percent and get 0.1 percent. When we have mutually exclusive events, meaning either one or the other one could happen, they both cannot happen at the same time, if we're concerned with the probability of A or B, it's simply the probability of A plus the probability of B. The key word to know that we're going to use the addition rule for mutually exclusive events is the word or. Let's take a look at an example. Let's suppose there is an investigator who is planning to run an experiment and they wish to select two machines randomly from the 10 units on the floor, and they're going to use these randomly selected machines for further testing. If each machine is numbered from 1-10, what's the probability that machine 4 or 8 will be selected on a single draw. Both the probability of getting machine 4 or machine 8, is the probability of 4 plus the probability of 8. In this case, the probability of getting machine 4 is 1 out of 10 and the probability of getting machine 8, is 1 out of 10. We add those together to get 2 out of 10 or two tenths, in decimal form this be 0. 2. In percentage form it's 20 percent when we have non-mutually exclusive events, meaning they could happen at the same time, the probability of A or B is equal to the probability of A plus the probability of B minus the probability of A and B. This would be the area visually, where these two events could overlap. Let's take a look at an example. Let's say we have a mixed lot with the following characteristics, and this lot could be parts. We have parts from vendor A, and parts from vendor B, and in these parts we have certain percentage defective, certain percentage not defective, and a certain percentage from vendor A and vendor B. We might want to know what the probability would be on a single random draw of selecting apart from vendor A or a defective part. If we were to simply use the probability of A plus the probability of B, this would be 100 over 165. And if we refer back to our contingency table, we can see that Vendor A has 15 plus 85, which equals 100 parts and the defective parts, we have 25 total defective parts. I would do 100 over 165 plus 25 over 165. That would give me 125 over 165, which is 0.758 percent. However, note that there are 15 more parts credited to the total than should be, because we have the probability of getting both Vendor A and the probability of getting defective at the same time, which is this right here, this 15. I'm going to take out the probability of getting both vendor A and defective, which is 15 over 165 and I'll use the formula for non-mutually exclusive events when we have the addition rule and we're looking at the probability of A or B. When I do so now, I'll subtract the 15 over 165 and end up with 110 over 165 and get a value 0.667.
