Augustina plays a game where she draws one card from well shuffled standard deck of 52 cards she wins a game if the card she draws is an eight or a face card for this problem let event n be the event where Augustina draws an eight and let event F be the event where Augustina draws a face card so we're going to start off by finding the probability of N and F okay so that's the probability that the card draws is both an eight and a face card so I have a deck of cards here it's a little small but hopefully it will do here's the trick for this one here are the eights right right there there's the eights and over here are the face cards okay so if we want to find the probability that Augustina draws an eight and a face card that that one card she draws is both of those things we just need to count how many cards are both of those six well I have four eighths I have 12 face cards but there are no eights that are face cards there are no face cards that are eight there are zero cards that are both V6 so there is zero chance that the card that Augustina draws is both an eight and a face card there's zero chance of that happening so now that we know that are the two events mutually exclusive well this is the condition of being mutually exclusive if it is impossible for both things to happen at once then the events are mutually exclusive mathematically that means the probability of nnf happening at the same time is zero and that's exactly what we have so the two events are mutually exclusive because it is impossible to draw a card that is both innate and a face card it is not possible to draw one card that both of those things so since the events are mutually exclusive which formulas are correct so we have our two addition rules this year okay this addition rule is always always always always true no matter what this Edition rule is true and so I'm going to check because I know it's always true but this second rule only applies when events are mutually exclusive in this case the two events are mutually exclusive we've already determined that so both of these rules are true both of these rules apply so now we have that what is the probability that Augustina wins the game um so how do you shoot one again she wins if she draws an eight or a face card so the probability that Augustina wins is equal to the probability that she draws an eight or a face card okay now this is an or probability and so we can use our addition formula here and because the events are mutually exclusive either one of these formulas will work because both work I'm going to use the simpler one probability of n plus probability of f okay now I do have to take the time to calculate this myself so the probability that she draws an eight well there are 4 8 in a deck out of 52 cards total ability that she draws a face card there are 12 face cards in a deck out of 52 cards total and all I'm doing here is doing what we usually do I'm counting these guys up they're 4 8. they're 12 face cards and I'm putting them over the total since the outcomes in this case are equally likely I can do that and be okay all right and so let's throw that into our calculator here 4 out of 52 plus 12 out of 52. evaluate that I get 0.3076923 so that means there is about a 31 chance that Augustina is going to win the game I'm going to copy this whole thing and paste it right here okay so that's the probability that Augustina wins the game we still need to find the probability that augustino loses the game we're going to look at that in a future video