 Okay, so complimenting events and playing cards. Today we're going to talk about probability, and we're going to discuss complimenting events. So my experience as a teacher, I found that this is a topic that a lot of students struggle with. So I thought I'd do a video on it. This isn't the most complicated problem, but I think it illustrates the point well. So let's say we're going to play some cards. We're looking at a standard deck of playing cards. It's 52 cards. And actually here I can show you what the standard deck of cards looks like. So we have our aces, twos, through tens, our jack, queen, and king. And we have our four suits. Here we're interested in if you draw one card from a deck of playing cards, what is the probability that it is not a heart? So we do not want to draw a heart. So I'm going to approach this problem using the compliment rule. So I'm going to look at the probability that I draw a heart. So up here are my hearts. I can count here. There are 13 hearts. So there are 13 ways to succeed, 13 ways to draw a heart out of 52 possible outcomes. So you have a 13 and 52 chance of drawing a heart, and this would reduce to one out of four. So you'll draw a heart about every four times. So I'm going to employ the compliment rule. The question isn't asking about drawing a heart. The question is asking about the probability of not drawing a heart. So the compliment rule, we look at the opposite. We know the sum of all possible probabilities will be one. So we're going to do one minus the opposite, the compliment of not drawing a heart, which would be drawing a heart. So we know the probability of drawing a heart is one out of four. So we're looking at one minus one out of four, which would equal three out of four. So the probability of not drawing a heart would be three out of four. Some students look at this problem and they want to solve it directly, or they think about solving it directly. If you solve it directly, if you think about not drawing a heart, drawing a spade, a diamond, a club, that would be three fourths of the card. So if you look at this problem directly, the probability of not drawing a heart would be three out of four. Or as you can see here with the compliment rule, the probability of not drawing a heart would be three out of four.