before we start some math let's just clear up a little myth no complimentary events are not those days when somebody said hey I really like your hat or you look like you've lost some weight although those are pretty nice events but in math they're not complimentary instead you can think of complementary events as kind of the opposite of what you're actually looking at so if you have a pizza on the table with eight slices and I take away two slices the complimentary event is leaving six slices behind I've taken two away that's the event we're looking at but the complimentary event is like it's like the opposite so two slices removed while the complimentary event means six slices left behind or another way to look at it let's say you watch TV for four hours a day well the complementary event of that is you didn't watch TV for 20 hours out of the day actually that sounds a lot better so the complement is the opposite so with that in mind let's have a look at our problem a standard deck of cards has 52 cards in a what is the probability of drawing an ace from the shuffled deck of cards and then in B this is where the complement comes in what is the probability of drawing anything but an ace all right let's get started with a remember the rule for finding probability well we're building a fraction but do remember what's on top and what's on the bottom let's review that the fractions that you build always look like this on the top we have the number of events being watched divided by the number of possible events there are so for a the number of events being watched what is that well we're looking for the probability of drawing an ace so we're watching for aces now how many aces are in a deck of cards well there's the clubs spades diamonds and hearts that's four there's four suits in a deck of cards and there's an ace for each suit so there are four aces the number of possible events well how many cards could you possibly take out of the deck at random there's 52 cards in the deck so that's the possible events there's 52 possible outcomes when you reach it and grab a card at random so 4 out of 52 so we should show that by saying the probability of an ace is 4 out of 52 for possible aces out of a deck of 52 cards now I'm not quite done can I reduce this well yeah I can 4 divides 52 13 times so that will reduce to 1 over 13 and that's my answer for a alright let's tackle B the trick for using the complement when probability questions is knowing that the rules for probability say that all possible outcomes must add up to 1 and when you reach into a deck of cards there's only two possible outcomes in this question either you get an ace or you don't get an ace so both of those must add up to 1 here's how we can write the complement of getting an ace the probability of not ace in other words probability of not getting an ace is equal to all possible outcomes which is 1 and we subtract from that the possibility or probability of getting an ace and we know the probability of getting an ace we found it in part a so the probability of not getting an ace is 1 minus 1 over 13 it now becomes a bit of fraction math we have to subtract two fractions since the 13 on the bottom I need to use that as my common denominator to turn this one into something with a 13 on the bottom I'm going to multiply the top and bottom by 13 it's going to look like this 13 over 13 is equal to 1 over 13 and now it becomes much easier 13 minus 1 is 12 so the probability of not getting an ace in a deck of cards is exactly 12 over 13 all right so remember that trick whenever you're asked to find the probability of something not happen usually it's easier to take a step backwards and find the probability of it actually happening then we take one and then subtract the answer that we just got and that'll tell us the probability of something not happening and we subtract the probability of it happening from one because the rules say that all things all possible outcomes in probability must add up to one and with that in mind let's get you to practice finding the probability of complementary events here's your question a bag contains 12 identically shaped blocks three of which are red and the remainder are green the bag is well shaken and a single block is drawn in a what is the probability that the block is read in B what's the probability that the block is not read remember that tip for finding things that are not okay try that one now and I'll post the solution when you're ready for Part A the probability of reaching into the bag and getting a red block was found to be 3 over 12 and reduce reduce that to 1 over 4 for B the probability of reaching into the bag and not getting a red block was found to be 3 over 4 and we did that by doing 1 minus our answer for Part A which was 1 over 4 so 3 over 4