let's go ahead and do a problem together as an example and we'll do one in my open math so we get a feel for it you draw one king from a well-shuffled standard deck of 52 cards let R be the event of drawing a red card and let K be the event of drawing a king we want to find all the following okay so we have lots of things to find here let's do it in order let's start with n of s so what does that mean again remember the n in front means number of and S is sample space so we want the total number of outcomes in the whole sample space What's the total number of outcomes all together well it's a 52 card deck and we're drawing a card so there are 52 ways total to draw a card from the deck okay so that one is pretty straightforward so let's go to the next one okay now we want n of R the number of ways we could draw a red card from the deck okay so how do we calculate that well it helps if we actually have the deck in front of us we want to find n of r and here are the red cards right here and you could either count them directly right or you can just know that there are two suits here and each suit has 13 cards 2 times 13 would be 20 26 cards 26 six cards that are red so the number of ways that we could draw a red card 26. okay there are 26 ways that we could draw a red card any one of those 26 cards would satisfy this event 26. let's calculate the probability of drawing a red card okay now drawing cards from deck in that case each outcome is equally likely there's not one card that's more likely to happen than another right if you've shuffled the deck well each card has the same chance of being drawn so the probability of drawing a red card we calculate use our formula the total number of cards that are red divided by the total number of cards in the sample space now we've already done the hard work for this we've calculated this and we've calculated this the number of red cards that's 26. the total number of cards in the deck that was 52 remember so 26 over 52 and if we put that into our calculator 26 divided by 52 we get 0.5 okay 0.5 and that makes sense right just looking at this if we Circle those red cards again that looks like half the cards in the deck okay so there's a the probability of drawing red card is 0.5 meaning there's a 50 chance that the card we draw from well Shuffle deck is a red card okay let's look at the other one n K and K is the number of ways we could draw a king okay so again we look at the deck and we just have to count them up okay nothing fancy going on here we're just counting here's the Kings over here and they're pretty easy to count there's one two three four Kings all together okay and that's it the number of Kings is four there are four outcomes that re result in us getting a king okay there are four ways to draw that draw King from the deck so now that we have that is four let's calculate the probability of drawing a king okay probability of drawing a cube okay so we use our formula and if K number of kings are divided by n of s total number of outcomes in sample space there are four kings in the deck out of 52 cards total to choose from and so if we throw that into our calculator 4 out of 52 we get this number line 0.07692308 so 0.07692308 if I wrote that right which is about like 7.7 if we were to think that as a difference so less than 10 so there's a less than 10 percent chance that the card we draw is a king that that makes sense if we look at this right if we look at the Kings most of the cards are not Kings those kings only make up a very small portion of the whole deck and so we would expect the probability of drawing a king to be fairly small and we have it right