Punnett Square Probability

in this video, we're going to begin our lesson on pun it square probability or probabilities that relate to pun. It squares now throughout this lesson, we're going to relate the probability of coin flips to the probabilities of pundits squares and the reason that we can relate The probability of coin flips to the probabilities of punnett squares is because they're representing independent events, and so two events are independent of one another. If the outcome of one event does not affect the outcome of the other event, for example, the outcome of one coin flip does not impact or affect the outcome of a second coin flip. Just like the outcome of one fertilization event does not impact or effect the outcome of another fertilization event. And so that's why, again, the probability of coin flips can be related to the probabilities upon it Squares now moving forward throughout this lesson, we're going to introduce and explain to different rules when it comes to the probabilities upon it squares and the first rule is going to be the rule of multiplication. Whereas the second rule that we're going to introduce is the rule of addition. Now, the rule of multiplication or the rule of addition can be used to determine probabilities and to predict genetic crosses. And again, we'll explain and introduce these rules as we move forward in our course in their own separate videos. But for now, notice down below What we're showing you are independent events of these coin flips of these two coin flips. And so notice over here we're showing you coin flip number one and coin flip number one has a 50% probability of landing on heads and another 50% probability of landing on tails. And so again, 50% is the same as one half. And then over here, what we're showing you is coin flip number two and coin flip. Number two is an independent event from coin flip number one, because the outcome of coin flip number one does not impact or affect the outcome of coin flip number two. And so when we flip coin number two, there's still a 50% probability that it will land on heads and a 50% probability that it will land on tails. And so you can imagine that these coins here represent ah Leal's and so when you do that. You can use the coins to, uh, generate a pun it square as we can see here. And so you can see that this square here is representing the possibility of both coins landing on heads. Uh, this one is representing the possibility of one landing on heads, one landing on tails. This one's the probability of landing one on tales one on heads and this one's the probability of both of them landing on tails. And so again, we are going to be relating the probability of coin flips to the probabilities of pun. It squares as we move along through this lesson. And so this year concludes our introduction to pundits square probabilities. And again, in our next lesson video, we're going to introduce and explain the rule of multiplication. So I'll see you all in that video

In this video, we're going to introduce the rule of multiplication, which is also sometimes called the and roll. Now the rule of multiplication, as its name implies, is going to involve multiplication. And the rule of multiplication is also sometimes called the product role or the end of roll. Now we'll explain why it's called the and roll here very shortly later in this video. But the reason it's called the product role is because the product is the answer to a multiplication problem. And so, by saying product roll, it's really just, uh, implying that multiplication is involved. And so the rule of multiplication, the product rule and the and rule are all referring to the same exact thing. And they basically say that the probability for multiple independent events, or the probability for greater than or equal to two independent events to occur together is calculated by multiplying the chances that each event occurs alone. And so, for example, the probability that two coins, coin number one and coin number two both land on tails. We need to take the probability of one coin landing on tails alone and multiply it by the probability of another coin landing on tails alone. And when we do that, we get one half times one half, which is equal to 1/4. And so again, the reason that this rule of multiplication is called the and rule of times is because the word and is usually used to refer to two events occurring together. So, for instance, coin one and coin too, both landing on tails. And so if we take a look at our image down below, over here on the left hand side, we're showing you, uh, these probability of flipping two coins at once. And so if we flip the first coin, we know that there's a 50% chance of landing on heads and a 50% chance of landing on tails or one half probability of landing on tails. But again, we're focusing here for the sake of this example, the probability that two coins both land on tails so we only have it labeled for the tails. We know that there's a 50% chance that coin number one will land on tails when we flip it. Then when we flip coin number two, it's a completely independent event. So the result of coin one is not going to impact the result of 10.2, So there's still a 50% chance that coin to will land on heads. I'm sorry on tails or on heads on DSO. What we need to do is if we want the probability that both coins will land on tails together. This is where we need to implement the rule of multiplication. And so we take the probability of one coin landing on tails alone, which again the first coined the probability that it lands on tails alone is one half. And then we take the probability that the second coin lands on tails alone, which is still one half. And if we want the probability that these two coins will both land on tails together, then we multiply these two probabilities one half times one half, which gives us 1/4. And so there's a 1/4 probability that both coins will land on tails. And that's exactly what we see here in this square that there is a 1/ probability that both coins will land on tails. Now over here on the right hand side, what we're showing you is another application of the multiplication rule by looking at this particular example, which says if hetero zegas parental pea plants have to offspring, what is the probability they will both be green? And so what we need to realize is that one fertilization event is independent from another fertilization event, and Soto have to offspring. We are really talking about two fertilization events that are independent of one another. And so, of course, when we take a look at this planet square, we're looking at a parent number one, which is hetero zegas parent number two, which is also hetero zegas. We fill in the pundit square and this is the probability that we see. And the probability that one offspring will be green, we know is one out of four total possibilities. 1/4 eso. We can even fill in 1/4 probability that it will be green, that one offspring will be green. But this is looking at the probability that two offspring will be green, not the probability that one offspring will be green. What's the probability that one off the first offspring will be green, and the second offspring will also be green, also known as the and roll here and so to do that, what we need to do or consider is the probability that the first offspring is green. So probability of offspring number one being green is 1/4. And because each fertilization event is independent, the probability that offspring number two is green is also 1/4. And so if we want the probability that both offspring are going to be green, then we need toe implement the multiplication rules. So we take the probability off one independent event and multiply it by the probability of another independent event. So 1/4 times 1/4 is actually one 16. And so the probability that both offspring are going to be green is 1/16 on. That is the answer to this example. Problem right here. And so this year concludes our introduction to the rule of multiplication, the product rule and the and rule, and we'll be able to get some practice applying these concepts as we move forward in our course. And then we'll talk about the rule of addition. So I'll see you all in our next video

So now that we've covered the rule of multiplication in our previous lesson video in this video, we're going to introduce the rule of addition, which is also sometimes referred to as the or role Now. The rule of addition, as its name implies, is going to involve addition. And the rule of addition is also sometimes called the some role or the or role. Now again, we'll explain why it's called the or rule a little bit later here in this video. But the reason it's called the some rules because the sum is the answer to an addition problem. And so the sum is implying addition now, the rule of addition, the some role and the or a role are all referring to the same thing. And really, what they say is that the probability that one independent event or another independent event will occur is calculated by adding their probabilities. And so this is another reason why it's called the or roll. It's because it's involving the probability of one event or another event. And so, for example, the probability that two coins will both land on heads or both land on tails is going to be the probability of one event, plus the probability of another event. So the probability that they both land on heads is 1/4 and the probability that they both land on tails is 1/4 and so the probability that one or the other will occur is 1/4 plus 1/4 and 1/4 plus one. Fourth is, of course, 2/4 and to fourth is the same exact thing as one half. And so there's a 50% chance of two coins landing on heads or two coins landing on tails. And so if we take a look at our image down below, over here on the left hand side, we could get a better understanding of that example with the coins. And again, we know that the first coin flip has a 50% probability of landing on tails, 50% probability of landing on heads and the second coin flip has a 50% probability of landing on heads and a 50% probability of landing on tails since they are independent events. And so if we want the probability that both coins will land on heads, then we need to take the probability of one coin landing on heads and multiply it by the probability of another coin landing on heads and so one half times one half is 1/4. And so the probability that both coins will land on heads is 1/ probability. And the same goes for both coins landing on tails. The probability of one coin landing on tails is one half the probability of another coin landing on tails is one half. And so the probability that both of these coins will land on tails together is one half times one half, which is 1/4. And so the probability that they both will land on heads this 1/4 the probability that they will both land on tales this 1/4. However, to get the probability that the coins will land both on heads or both on tails, we need to take the probability of these occurring independently and add them together. And so the probability of both of them landing on heads is and the probability of both of them landing on tails is one for And so if we want the probability of them landing on heads or landing on tails, then we add them together. And so notice the addition sign here. And 1/4 plus 1/4 is again 2/4 which is the same thing as one half. And so there's a one half probability of them, both of them landing on of them, both landing on heads or both, landing on tails. Now, over here on the right. What we're showing you is another application of the addition role as it applies to this particular example, which says to calculate the probability of having a home mosaic is dominant or a Homo Ziggy's recessive offspring. And so, of course, when we take a look at this pundit square, the probability of getting a Hamas, I guess dominant offspring is 1/ and the probability of getting a Homo zegas recess of offspring is also 1/4 However, to get the probability of getting a Hamas August dominant or a Hamas August recessive, we need toe add these probabilities together, and so the probability that the offspring is home mosaic is dominant is 1/4 the probability that the offspring is Homo zegas process. It is 14 and if we want the probability that one event or the other event will occur. We need to add them. And that's again while we have the addition sign here. And so 1/4 plus 1/4 is to force, which is the same thing as one half. So there's a one half probability, or a 50% probability of the offspring being either Homo Zegas, dominant or homos, I guess. Recessive and with one half here is the answer to this example problem. And so this year concludes our introduction to the rule of addition or the some rule or the aural, and we'll be able to get some practice applying these concepts as we move forward in our course, So I'll see you all in our next video.