 ## General Biology

Learn the toughest concepts covered in Biology1&2 with step-by-step video tutorials and practice problems by world-class tutors

13. Mendelian Genetics

# Punnett Square Probability

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## Punnett Square Probability 3m
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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
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## Rule of Multiplication (the AND Rule) 6m
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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
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Problem

Calculate the probability of 2 heterozygous (Rr) parents having 3 homozygous recessive (rr) offspring.

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## Rule of Addition (the OR Rule) 5m
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Problem

What is the probability that a plant from a monohybrid cross of heterozygous parents, is homozygous dominant OR homozygous recessive?

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Problem

A blue-eyed female that is homozygous recessive and a brown-eyed male that is heterozygous mate, producing two offspring. What is the probability that one child will have blue eyes AND one will have brown eyes? (Eye color is controlled by a single gene).

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A homozygous dominant male has a child with a heterozygous female. What is the probability that the child will have the same genotype as its father OR its mother? 