 In this video, we provide the solution to question number 12 for practice exam number four for math 1030 in which case we're given a standard deck of 52 playing cards and we have to compute the probability of a specific event. Now if you're not familiar with how a standard playing deck is organized, there is a description right here on the screen. It talks about the four suits, the two colors, the 13 cards, what's a face card, what's a high card, things like that. If you're still not familiar, there is a link to this video in the description that can take you to explain you more how these decks of cards are organized. Now for the sake of this video, I'm just going to talk about the probability and not the organization of this deck. So assuming that the deck is well shuffled, that is, any card is equally likely to be dealt here, then what is the probability of the following event of drawing a red card or a diamond, a red face card or a diamond, okay? So let's think about what, how, how would you draw these? There's two events here. We'll call this event E and this event F. So what is the probability of event E? Like so. So there's 52 cards total, just so you're aware. If we're looking for a red face card, there are three face cards, the jack, the queen and the king. And red, there's two suits that are red. There are hearts and there are diamonds. So the hearts have three face cards. So there's the jack of hearts, the queen of hearts, the king of hearts. The diamonds also have three face cards. There's the jack of diamonds, the queen of diamonds and the king of diamonds. As such, there are going to be six cards which are red face cards. So that's the probability of the first event happening. The probability of the second event, again, it'll be out of 52 cards. It'll be out of 52 cards. So the question is how many diamonds are there? Well each suit, diamond is one of the suits. There are 13 suits totals, so you're going to get 13 out of 52. So that's the probability of those events happening. Now what we're looking for is the probability of or here. So we're looking for the probability of E or F happening. Okay, so by the principle of inclusion, exclusion, we take the probability of E plus the probability of F and then we have to subtract from it the probability of E and F happening, their intersection there. So we have most of these numbers already. We have six over 52. And then over here, this last one, what's the probability that we draw an and statement? So we're looking for a red face card and a diamond, okay? Well, the only face cards that are red and a diamond is going to be the jack of diamonds, the queen of diamonds and the king of diamonds. So we're going to have three out of 52 like so. And so simplifying this thing, notice that if we take 13 minus three, that's going to give us 10. 10 plus six is 16. So we're going to get 16 over 52, like so. 16 and 52 are both divisible by four. Four goes into 16 four times. Four goes into 52 13 times. So we see that the correct probability is going to be four out of 13, which gives us choice A.