hi it's mr. Andersen today I'm going to be talking about multiplication and addition you might think that's a little simple for what I usually talk about but I'm going to talk about how we can apply multiplication and addition to genetics and unlike in math I'm going to start with multiplication because it's actually easier that way multiplication is going to occur in genetics if we ever have independent events that are going to occur in sequence another way to tip yourself off to that is if in the question it's saying the word and so let me give you an example of that what are the odds of flipping a coin five times and getting tails on every flip well you can use the rule of multiplication to figure that out so what are the odds of getting a tails on one flip of the coin that's just one in two so all you do is you multiply all the probabilities out one two and that's going to be one and four eight 16 so that's a 1 in 32 probability of flipping the coin five times in a row and getting tails every time same thing would be true if we were to say you're going to have five kids what are the odds of all of them being boys it's just multiplying the probability of each of those events because they have to occur in a specific sequence so let me show you how we could apply that to a couple math and then genetic problems and so you may want to as you watch the video pause the video after I present the questions try to work them on your own and then I'll go over the right answers so here's the first to number one rolling Snake Eyes on two pair of dice so how do we do that well there are six sides to a dice a one is going to occur on one out of every six of those sides and so it's a 1 in 6 probability of rolling a 1 on 1 dice times a 1 in 6 probability on the other dice and so the right answer would be 1 in 36 so it's going to be rare that you get Snake Eyes roughly 3% of the time less than 3% of the time let's go to the next one what are the odds of picking a 3 out of the deck we're turning it to the deck and then picking a king out of the deck how do you solve this one well you have to look at each of those different events because they're happening independently up one another what are the odds of picking a three out of a deck well there are four threes in a deck of normal playing cards there 52 and so to save myself a little bit of time I'm going to reduce that so that's one in 13 probability of picking out a three since you're returning it to the deck there are going to be 52 cards again so the odds of getting a king out of the deck are also going to be one in thirteen and so the odds of doing both of those in succession is going to be one in 169 so it's going to be really really rare okay so that's math now let's apply it to genetics let's say I apply it to the work of Mendel so in this first problem in a cross between pea plants that are heterozygous so they're hybrid for a purple flower what's the probability that the offspring will be homozygous recessive okay so how do we do that well we first write each of the parents so big P little P crossed with big P little P so what are the odds that this parent over here since we're looking for a homozygous recessive to build that we have to get a little P little P so what are the odds that this parent is going to contribute that little P well that's a 1 into probability what are the odds that this other parent is also going to give a little P well that's a 1 in two and in order to get that homozygous recessive we have to have both those occurring so we simply multiply those or that's going to be a one-in-four probability now you might think to yourself this is easy I could do this with a simple punnett square but the next problem is going to show you how important it is to learn to do multiplication so here's question 1 or question 2 in a cross between this parent and that parent what is the probability that the offspring will be this this is a question that I love to ask on my tests and the AP Biology folks love to ask as well because when you see a question like this some people just shut down because they see it's a tri hybrid cross they're imagining like an 8 by 8 punnett square impossible to solve and so if you use the rule of multiplication it's actually really simple and so all you do is work a letter at a time so what I'm going to do is I'm going to concentrate on the A's these two so these parents what are the odds that I'm going to get that offspring and so I could just do this in my head I know this is a 1 in 2 probability if you can't do that do a little punnett square so this would be one parent this would be the other parent and so that's going to be a big a big a this is going to be a big a little a big a little a little a so the odds of getting a big a little a is going to be a 2 and a 4 or a 1 in 2 probability now let's just work on the B so with that parent and that parent what are the odds that we're going to get this well this one is always going to give a big B this one will give Big B half the time and a little be half the time so the odds of getting that are also going to be 1 and 2 what are the odds of getting a Big C Big C well same thing this one allow is give a Big C do a Punnett square if you've confused this one will give a Big C half of the time little C half of the time so that's also 1 and 2 probability so what are the odds of me getting this from those two parents I just multiplied those because all three of those have to happen and so there's a 1 in 8 probability that you're going to get an offspring that looks like that and so that's a solvable problem so you should practice a few of these but it's a good way to understand what you could get for answers and not having to build some kind of unwieldy punnett square next let's go to addition the rule of addition occurs the tip-off is going to be if you see the word or in the question but it occurs when we have mutually exclusive event so two things that could go either way so again let me give you an example of that let's say I flip the coin again what are the odds that I'm going to get either a heads or a tails well how do you solve that that seems you could just answer it just thinking about the question but what are the odds I'll get a heads so 1 into what are the odds that I'll get a tail a 1 and 2 and so when I say what are the odds of getting the heads or a tails you can build it in two different ways and so we're going to simply add those up so it's a 1 in 1 probability or probability of one or a hundred percent of the time you're either going to get a heads or a tails so that's kind of when we use addition let's do a couple of math problems to kind of sort that out number one what are the odds of rolling a 2 or a 5 on a six-sided die so again you may want to pause the video try this one out what's the odds of rolling a 2 or a 5 on a six-sided dice well the odds of rolling a 2 are 1 in 6 odds of rolling are a 5 or 1 and 6 and so we simply add those together so that is a 2 + 6 or a 1 in 3 probability of getting a 2 or a 5 let's go to the next one which is a little bit harder what's the odds of picking a 5 or a heart out of a deck of playing cards so again we're going to be using the rule of addition let's start on the 5 so how many fives are in the deck 4 so there's 4 out of 52 probability of picking a 5 what are the odds of picking a heart well there are 13 hearts in the deck and so you may be tempted to just add 13 to it but we've already eliminated one of those hearts because we chose the 5 of hearts and so that's going to be 12 out of 52 since we eliminate that and so that's going to be a 16 out of 52 which reduces to 802 26 or 4 out of 13 probability that if you pick a card out of the deck it's either going to be a 5 or a heart okay so that's math now let's apply it to science let's say it applied specifically to genetics so in this question in a cross between pea plants that are heterozygous for purple so we're going to have the same parents here what are the odds that the offspring is going to be heterozygous so what are the odds what we're looking for is an individual it is this for our offspring okay so how do we do that well let's first of all build it one way so we could get this one could give the big P and this one could give the little P so that's a 1/2 probability 1/2 probability of that and so that is a 1 in 4 probability to build it this way but this one over here could give its little P and this one could give its big P and so that would be another way we could build it so let me write those over here what are the odds of that well that's also going to be a 1 in 4 because there's a half on this and a half on that and so the question is saying what is the probability of being heterozygous since we can build it in two ways we are going to add those up and so there's a 1/2 probability and so when you look at a punnett square punnett square visually shows you that but if you use the rules of addition then you don't have to do a lot of work so let's do the last one so this is the final question if you can if you can answer this one you can you're accurately using the rule of multiplication and the rule of addition so in this one we're crossing this parent they're heterozygous for everything with this parent what are the odds that we would either get this or that okay so this is we're gonna have to apply everything to it so let's start with the a so if we go with the A's what are the odds with that parent in that path that we're going to have this well that'd be a one-in-four probability and since I'm looking at the a so let me go to the next day it's going to be a one-in-four probability over here let's look at this B with this parent and that parent what are the odds that we're going to have that well that would be a 1 in 2 probability over here and over here that's also going to be a 1 in 2 probability now let's look at the C so with that parent and that parent what are the odds that we're going to get that well that is a 1 in 2 probability on that one and over here it's going to be a 1 and 2 probability as well and so what are the odds that we're going to both of those well this one is going to be I'm just checking again to make sure that all right yeah looks good so we're going to multiply these all up so that's 1/4 times so that's an 8 times 16 so 1 in 16 odds over here we're going to add that up because we got the war in there so that's going to be a 1 in 16 over there so it's going to be a 2 in 16 or a 1 in 8 probability that we're going to get that and so again if you can apply the rules of multiplication if you can apply the rules of addition to genetics that's going to make your life a lot easier and I hope that's helpful