in this video we're going to focus on probability word problems a jar contains seven red marbles six green marbles five blue marbles and two yellow marbles what is the probability of selecting a green marble well let's make a list of the different colors that we have so we have red we have green blue and we have yellow so there are seven red marbles six green marbles five blue marbles and two yellow marbles now let's add up these numbers 7 + 6 is 13 13 + 5 is 18 18 + 2 is 20 so there's a total of 20 marbles in the jar now if you want to calculate the probability of getting let's say a green marble what you need to do is find the number of of green marbles in the jar there's six green Marbles and divided by the total number of marbles which is 20 so the probability is 6 out of 20 but of course we can reduce the fraction since both numbers are even we can divide them by two half of 6 is three half of 20 is 10 3 over 10 is basically 3 as a decimal which is equal to 30% so there's a 30% chance of selecting a green marble from this jar now what about the Blue Marble what is the probability of selecting the Blue Marble so how many blue marbles are in the jar notice that we have five in the jar out of 20 so the probability is 5 over 20 so now let's reduce the fraction by dividing each number by five 5 ID 5 is 1 20 ID 5 is 4 1 over 4 if you type it in the calculator is 0.25 as a decimal which correlates to 25% so there's a 25% chance of selecting a Blue Marble now if there's a 25% chance of selecting a a Blue Marble what is the probability of not selecting a Blue Marble to find the probability of not selecting a Blue Marble it's going to be one minus the probability of selecting a blue marble and is U the probability of selecting a Blue Marble is 0.25 1 minus 0.25 is equal to 75 which is 75% so if there's a 25% chance of selecting a blue Mar marble then there's a 75% chance of not selecting a Blue Marble if there's a 30% chance of selecting a green marble then there's a 70% chance of not selecting a green marble let's clear away a few things now let's talk about another way in which we can calculate the probability of not selecting a green marble the other technique involves finding how many marbles are not green so we have seven 5 and two so that's 7 + 5 is 12 12 + 2 is 14 so there are 14 marbles that are not green out of a total of 20 and so let's go ahead and reduce this fraction so let's divide both numbers by two 14 / 2 is 7 20 / 2 is 10 and so we get 7 out of 10 which is 7 and 7 if you multiply by 100 this will give you 70% so as you can see there's a 70% chance of not selecting in a green marble now let's get rid of this now let's move on to the next part part C what is the probability of selecting a green or a yellow marble how can we figure this out if you see an or statement It's associated with the sum the probability of selecting a green or yellow marble is equal to the probability of selecting a green marble plus the probability of selecting a yellow marble so we just got to add these two values and it's going to give us the answer so there are six green marbles out of a total of 20 and to find the probability of selecting a yellow marble we can see that there are two yellow marbles in the jar of 20 marbles so it's 2 over 20 now since the denominators are the same in these two fractions we can go ahead and add them 6 + 2 is 8 so it's 8 over 20 now 8 and 20 are divisible by four so let's reduce the fraction so this is going to be 2 over 5 if you type 2 / 5 in your calculator or if you use long division you can convert this fraction into a decimal and so it's going to be4 4 which is uh 40% so there's a 40% chance of getting a green or a yellow marble now what about the next part what is the probability of getting a red marble and then a blue marble with replacement so this is basically an and statement we need to get ready and blue on the first try we need to get red and on the second try we need to get blue so the order matters here so what is the probability of getting a red marble on the first try by the way whenever you have an and statement you need to multiply if there's an or you need to add so just keep that in mind so we need to multiply the probability of getting a red marble the probability of getting a Blue Marble so what is the probability of getting a red marble on the first try so there's seven red marbles out of a total of 20 so it's 7 over 20 now what is the probability of selecting a blue marble with replacement with replacement means that once you take out the red marble in the first try you put it back in and then you want to see you know the chances of getting a Blue Marble on the second try so once you put the red marble back in there's still a total of 20 blue marbles and there's five I mean there's a total of 20 marbles in general and out of those 20 marbles we have five blue marbles I think I said 20 blue marbles but there's only five so once you put the red marble back in you still have 20 marbles in the jar now instead of multiplying across Let's uh cancel first we can reduce 5 over 20 we can divide each number by five so we can cancel a five from the top and the bottom so this is going to be 1 over four 7 * 1 is 7 4 * 20 is 80 so the answer is 7 over 80 and as a decimal this is equal to 0 875 which is uh 8.75% now if you're wondering what just happened I accidentally closed the application and so I'm just going to rewrite this information but let's work on the next part what is the probability of selecting a red marble and then a Blue Marble but this time without replacement so what do you think we have to do here feel free to pause the video and work on that example so we're still dealing with multiplication there's two events we need to get a red marble and a blue marble and anytime you're dealing with an and statement in regards to probability you need some multiply the two events together that is you need to multiply the probability of getting those two events so we need to get a red marble on the first try and then a Blue Marble on the second try so the probability of getting a red marble on the first try is still 7 over 20 so that part hasn't changed now what about the probability of getting a Blue Marble but without replacement without replacement means that after you take out the first red marble on the first try you don't put it back in it stays outside of the jar which means that we no longer have 20 marbles in the jar we now have 19 so therefore the probability of selecting a Blue Marble is five out of 19 since there's five blue marbles in a jar that contains only 19 marbles left over and so this is going to give us the answer 20 is basically 5 * 4 and notice that we can cancel a five which will make the math a lot easier so now on top is just going to be a seven on the bottom 4 * 19 4 * 19 is 76 7 divided by 76 is 092 so there's a 99.2% chance of getting a red marble on the first try and then a Blue Marble on the second try without replacement now what about the last one what is the prob ability of selecting a red marble and a Blue Marble without replacement so how is Part F different than part e go ahead pause the video and think about this problem see if you can get the answer try to work it out and then when you're ready unpause the video and see what the solution is so what's the difference between then and and now in part e on the first try you want to get a red marble and on the second try you want to get a Blue Marble in that order but in Part F the order is not specified so that means that you can get a red marble in the first try and then a Blue Marble in the second try or remember or means Plus or sum you can get a Blue Marble on the first try and then a red marble on the second try in Part F because the order is not specified it can be RB or BR so the probability of getting red on a first try and then blue on the second try we got that answer in the last problem it's 7 over 20 for the red marbles and then for the blue marbles it's 5 over 19 this is without replacement so don't forget to deduct this number by one now for br the probability of getting a Blue Marble on the first try there's five blue marbles out of a total of 20 and since it's without replacement once we take out the Blue Marble there's 19 left and the probability of selecting a red marble is going to be seven out of the remaining 19 so notice that these two answers are the same in both cases we're going to get the same answer of 7 over 76 that's the probability of getting red then blue and the probability of getting blue than red is also 7 out of 76 so you have to double the answer so it's 14 out of 76 and we can reduce this fraction we can divide the top and the Bottom by two so this is going to turn into 7 over 38 738 I mean 7 over 38 that's 84 as a decimal so there's an 18.4% chance of getting a red and a Blue Marble without replacement the probability of not getting a red and a Blue Marble without replacement is 100us 18.4 and that's uh 81.6% chance of not getting a red and blue so now let's review a few important details that's going to help you when solving probability problems so anytime you see the word or associate it with addition or sum whenever you see the word an associate it with multiplication so just keep that in mind so here's a question for you what is the probability of selecting a red marble then a green knobble not and so you want to get a red marble first and then a green marble on a second try or get in a blue marble and then a yellow marble on the second try so go ahead and try to figure this out so the probability of getting red and green we need to multiply so it's going to be P of R that's the probability of selecting a red marble and the probability of selecting a green marble so we're going to multiply by PG and then we have an or statement so that's going to be addition the probability of getting a Blue Marble that's PB and the probability of getting a yellow marble we'll call it a py so we're going to have to multiply it by py the probability of getting a red marble is 7 over 20 and let's say it's with replacement I forgot to specify that so with replacement the denominator will remain 20 so there's six green marbles out of a total of 20 and then plus the probability of getting a Blue Marble is 5 over 20 and of getting a yellow marble it's 2 over 20 now let's reduce the fractions that we have we can add them right now if we want to so you can reduce it now or you can add 6 * 7 is 42 let's add them first 20 * 20 is 400 5 * 2 is 10 so this is going to be 10 out of 400 42 + 10 is 52 so it's 52 out of 400 now we can divide both numbers by four 52 ID 4 is 13 400 ID 4 is uh 100 and 13 over 100 it's easy to see what the decimal value of that is that's 13 which is um 133% and so that's the answer that's the probability of getting a red marble on the first try then a green marble on the second try or getting a Blue Marble on the first try and then a yellow marble on the second try so that's it for this video hopefully it's been helpful for you um in dealing with probability problems so thanks for watching and have a great day