 Hi, this is an example on calculating probabilities using the conditional rule and more in the example I have 200 consumers who were surveyed about a new brand the snack food called crunch goals They give us a table here Notice they break down the information by age group and whether or not they liked or disliked crunch goals So we want to calculate the probability that the consumer is 18 to 24 years of age given that he or she dislikes crunch goals One signal phrase in this example would be the fact that they say given that What this means is that we have a conditional probability? What a conditional probability does is it shrinks the sample space down to the given that condition? The condition is that they dislike crunch goals. So out of this entire table the only row I'm concerned with Would be those that dislike crunch goals in total. There's 30 people that disliked crunch goals How many of those were 18 to 24 years of age? That would be eight So you have eight over 30 you can simplify this fraction to get four over 15 and part B What is the probability that the selected consumer dislikes for crunch goals? So we're using all of the data in the table the entire sample space of 200 people so out of 200 people my goal is to identify the Customers or consumers that disliked crunch goals so out of the 200 how many people dislike crunch goals that would have to be 30 30 out of 200 or Three over 20 Next what is the probability that the selected consumer is 35 to 55 years old or likes crunch goals? So this isn't or probability That means we do consider all 200 people from the table and The ones that we want the ones that are favorable outcome would be those that are 35 to 55 years old or those that like crunch goals So we're looking at 35 to 55 years old We are looking at those that like crunch goals This will give me my numerator so those that liked crunch equals I had one four one and six Those in the 35 to 55 age bracket. I already counted the one. I need to do seven and 46 So what this is going to give me is 65 over 200 Which can be simplified to give us 13 out of 40 and part D? If the selected consumer is 70 years old, what is the probability that he or she likes crunch goals? So what this is once again is since we have that if the selected consumer is 70 years old This is actually a condition. This is a conditional probability Where the condition given is that the selected consumer is 70 years old. Where does 70 years old fall? That would be the 55 and over age brackets. These are the only people I'm considering in this example in part D So in the 55 and over group I have a total of 28 people Favorable outcomes are those that like crunch equals So in the 55 and over age bracket how many people like crunch equals six? Simplify the fraction you'll get three out of 14. That is the probability. Thanks for watching