>>Probability is a measure of the likelihood of the occurrence of some event whose outcome is unknown. There is a particular vocabulary that goes along with the business of making the calculation of probability. Let's talk about the vocabulary a little bit then we'll get into some calculations of probability. Probability situations begin with some experiment. An experiment is just some activity where we can observe the outcome of the activity. For example tossing a coin we can observe in tossing the coin whether the coin comes up heads or tails. Rolling a die we observe the face of the die as it comes up and stops rolling. Drawing a card from a deck of cards, interviewing voters for their preference on a particular political candidate perhaps so all of these are various kinds of experiments. A sample space is a list of all possible outcomes and generally this list is put in to kind of a set format. So it's the set of all possible outcomes for some experiment. An event is one or more outcomes. Now it's starting to sound a little complicated and I think we take the complication out of it with an example. An experiment is like rolling a die. Now rolling a die you know that there are 6 faces on a die. It's just a little cube and you roll the cube and a 1 or 2 or 3 or 4 or 5 or a 6 can come up when the die finishes its rolling process. So the sample space all the possible outcomes would be the set consisting of 1,2,3,4,5, 6 and that's all there is to it. Now some events associated with this would be rolling a 5. That's an event. You see rolling an even number, that's an event. Rolling a number less than 3, all of these then are events associated with that experiment. Let's talk about probability. The probability that some event will occur is calculated as favorable outcomes, the number of favorable outcomes over the number of possible outcomes. So rolling a die if we want to find the probability that a 5 comes up when we roll then how many favorable outcomes are there? How many ways are there to roll a 5? Well there's only one way to roll a 5. There's only one 5 you see. And the number of possible outcomes well to find the possible outcomes you just count the items in the sample space. So there are 6 possible outcomes in rolling a die. So the probability of rolling a 5 is 1 over 6. Now probability numbers are written as fractions like this or they could be written as decimals or the decimals could be turned into percents. So a probability number could be a fraction, a decimal or a percent. What about the probability that an even number is rolled? Well let's see, the probability of even means favorable outcomes over possible outcomes. How many even numbers are there in the sample space? You see that's kind of what we're asking for the numerator of our probability fraction. Well there's 2,4, and 6 that are even numbers in the sample space so there are 3 even numbers out of the 6 possible outcomes. So the probability then is 3 over 6 or 1 half or 50 hundreds or excuse me 5 tenths or 50 hundreds or 50 percent, all mean the same thing. The probability that the number that we roll is less than 3, less than 3 that would mean it would have to be 1 or 2 so the favorable outcomes, there are 2 of them, the 1 or the 2. And the possible outcomes is 6 reducing we get one third for the probability. What about the probability that we roll a 7? Well gee 7 is not even in the sample space so this is not a possibility. So there are no possible favorable outcomes here you see, no way to roll a 7 and there are 6 possible outcomes so zero over 6 is zero. And the reason I put this example in here is because this is an impossibility and the probability associated with something which is impossible is zero. Now consider this one, the probability that the number that we roll is a one digit number. If we look at the sample space all of the numbers are one digit numbers. So this has to happen. This is a certainty. So there are 6 situations that will fill this out of the 6 possible outcomes. So the probability here is 1. So items which are impossible have a probability of zero associated with them and items that are certain have a probability of 1 associated with them.