Compound Probability with Dependent Events FULL LESSON WITH PRACTICE PROBLEMS AND SOLUTIONS

hey welcome back to mr. ace man this lesson is on compound probability except the only difference between this lesson and my other lesson is that the other lesson was on independent events where one event did not affect the other independent this is on dependent events in other words the first event will have some change on the second event some stuff you should know are the basics of probability what sample spaces are how to make and reach read agree and how to multiply fractions make sure you know these and let's get started so what exactly is compound probability well compound probability is probability that consists of what are called compound events and compound event is when you have more than one event where one occurs right after the other so basically just product of each of the individual events and dependent events are events where the first event does have an effect on the second you might have seen my other lesson that was on compound probability but that was independent it means they do not affect each other but dependent means that the first event will change the second event and you'll see exactly how that works so for example let's take look at some letter Styles let's say we have some tiles that spell out the word house and we're trying to find the probability without replacement now without replacement basically just means that you take out one from the first event and you don't put it back let's take an example let's say we want to find the probability of getting an from the word house and then the probability of selecting an from the word house we're trying to find the probabilities for each of the separate events so what's the probability of getting well there are five letters and there's one there so the probability of getting the letter is 1/5 now that we found the letter we're assuming that we've gone into the bag of letters house we've taken out an and we're not putting it back so now it's not there anymore so now we're not picking from five letters we're only picking from four letters so now what's the probability of selecting the letter well there's four letters and there's one so the probability of selecting now is one fourth now that I've got the probabilities of my two separate events just multiply them and 1/5 times 1/4 is going to be 120th so that is our probability so here we have the word class same exact concept as our last example we're trying to find the probability without replacement and that means we're going to take out one from the first event and then we don't put it back so let's say we're trying to find the probability of drawing two S's from the word class well you might not be familiar with the way it's written like right here you might be familiar with seeing the first event and then the word then and then the second event so what does two S's mean that just means we're trying to get an for the first event and then an for the second event so what's the probability of selecting an for our first event well there's five tiles in the word and there's two letter therefore the probability of drawing an is 2/5 now remember what we said without replacement means that we take out whatever we said we were looking for in the first event and then we don't put it back so we're saying that we're going to take out 1s from the first event and we're not putting it back so it's gone for good now what's the probability of selecting an for the second event well there's four letters there's one therefore the probability is 1/4 so now that know the probability of my first event here it's 2/5 and know the probability of my second event which is 1/4 just multiply them and 2/5 times 1/4 gives us to 20th but that's not in lowest terms that can actually be reduced so when we reduce that our final answer is 1/10 how about here we have the word networks now we're trying to find the probability of drawing vowel for the first event and then consonant for the second event so let's look at our first event the probability of selecting vowel well how many vowels are there is vowel is vowel and that's it so that's 2 out of how many letters well 1 2 3 4 5 6 7 8 we have tile so that's gonna be 2 out of 8 now it doesn't matter which vowel we select we just have to take one out and that's really really important to remember lot of my students saying well that means take out two absolutely not you're only taking out one from the first event and it doesn't matter which one the one you pick is irrelevant we could take out the letter or we could take out the letter it doesn't make difference but first let's reduce to three deuces to one-fourth so like said before we can take out any of the vowels we want so let's take out the letter and we're saying we don't put that by holdback so that's gone for good and now we're looking at second event the probability of getting consonant well how many consonants are there well and as consonant is consonant is consonant and are consonants so that's six consonants out of how many letters well we had eight before but one is gone now so we only have one two three four five six seven so the probability of drawing consonant is six out of seven and now that have the probability of my two separate events all do is multiply them and when multiply one 4 times 6 7 get 6 28 but that not in lowest terms so that can be reduced and when we reduced that our final answer is 3 for teens okay so we're still talking about probability without replacement but instead of talking about tiles I'm using something little bit more practical playing cards so here we have 5 cars and let's say we want to find the probability of getting red card and then black card well let's talk about our first event first their probability of getting red card okay well how many cards are there well there's five cars and of the five cars how many are red there's two red cars so the probability of getting red card is two out of five like said before we are not putting one of the cards back and we're only gonna take out one of the cars do we take out - no we are not taking out both of whatever our first probability is we're only selecting one of the red cars so let's say we took out the Kings card that's gone now and now we try to find the probability of getting black card so how many black cards are there well there's three black cards out of how many total cards four so the probability of getting black card is three out of four and then we just multiply our probabilities and that's gonna give us six over twenty but that's not in lowest terms therefore we'll just reduce and get three over ten and that is our final answer how about here we're looking to get the probability of two spades and like we said before you may not be familiar with this notation here it says two space we're not used to seeing compound probability like that we're used to having the first event and then second event well what exactly does it mean to find two spades that means our first event is gonna be speed and then we're gonna get speed for our second event so let's talk about the first event what's the probability of getting spade well there's only one Spade here the two of spades and how many cars are there that's five so the probability of getting spade for our first event is one out of five and now let's take that 2 of spades out so now what's the probability of getting spade well how many spades are there there is zero and we're gonna multiply our probabilities and that's going to be zero and that's called an impossible outcome now think about this for second if we get spade for the first card and then we took it out like we just did that's who spades is now gone can we draw second Spade no so would it be possible to draw spade and then second Spade after we removed that last Spade no we can't do it there's no way to draw two spades when you only have one therefore we got an impossible outcome in this example we're trying to find the probability of getting three black cars well like we said before you may not be familiar with this notation but what does it mean to get three black cars it means we have how many events well how many black cars are we trying to get three so we're gonna have three events and the three events will look like this is going to be the probability of getting black card for the first event black card for the second event and black card for the third event so let's deal with the first event the probability of getting black card is well what do you think there's five cards three or black the club this spade in this club so that's three out of five now let's take one of the black cards out because remember we're taking out black card one black card and not putting it back so let's take out the ace of clubs and move on to our second event which is probability of getting another black card well how many black cards are there there's two out of how many four so the probability of getting black card is two over four so let's take one of the black cards out now and we just repeat the process now we're looking for the probability of getting black card after that well how many cards are there there's three and how many are black one there for now on the third event the probability of getting black card is one out of three and then we just multiply our probabilities well we can still reduce the two fourths we can't reduce three-fifths that's already in simplest form the one-third here is also already in some of this form but to force can be reduced to 1/2 and then we just multiply three-fifths times one half is gonna give us three tenths and now we just multiply that with 1/3 and that's gonna give us three over 30 but three over thirty can be reduced so let's do that and when we do that we get 1/10 so the probability of drawing three black cars is 1/10 so here's your pause and practice just pause and practice when you're done unpause the video after 3 2 1 countdown your answers will be displayed go alright so let's see how we did number 1 is 5 over 22 number 2 is 1 over 11 number 3 is 8 over 33 number 4 is 1 over 66 and number 5 is 3 over 55 let's review an event that consists of more than one event or parsis called compound event in compound event when the first event does have an effect on second they are called dependent events remember it's very different from independent events where the first has no effect on the second such as flipping coin if you flip coin the first time and you do it again that first flip didn't mean anything not gonna affect your second event but here when we went over the tiles and taking one out and not putting it back those are all dependent events because the second event is affected by the first to find the probability of compound events you have to blank the probability for each event well we just multiply don't forget to like share and subscribe questions comments leave them down below and thanks for using mr. ace Matt don't just pass Matt ace it