in a previous video we went through a lot of work and we found the probability that Augustine wins a game probability that she won this particular game is 0.3076923 okay what we wanted to find out is what is the probability that Augustina loses the game the trick here trick here is knowing that winning and losing are complementary events they are the only two things that can happen here either Augustine is going to win this game or she loses this game there's no other option okay so in the language of mathematics we would say the complement of winning is losing and the complement of losing is winning what does that mean remember for complimentary events there mutually exclusive okay so that means probability of winning or losing is going to be just probability of winning plus the probability of losing but we can actually go a little bit further because these are complementary events when we put them together that's the whole sample space one of these two things has to happen so there is a 100 chance that she either wins or loses right 100 chance that one of those things happen and so instead of having this here I know this probability this probability is one or a hundred percent so I want to find the probability that she loses but I already know the probability that she wins okay so if I subtract that probability to the other side of the equation I find out that 1 minus the probability that Augustine wins the game is equal to the probability that she loses the game now I want to emphasize this using this using what we already know and we already know the probability that Augustine wins a game using the probability that we already know is easier than calculating the probability that Augustina loses directly because there are lots of ways for her to lose we know um she wins as she draws an eight or a face card okay but there's a lot of other cards for her to choose from right there's a lot of other cards for her to choose from and so it can be tricky to calculate the probability that she loses directly this is often an easier way to calculate the complement of a probability that we already know so in this case 1 minus the probability that she wins this is the probability that she wins okay so 1 minus that probability we get 0.6923077 that's going to be the probability that Augustine loses the game