Pedigree for determining probability of exhibiting sex linked recessive trait | Khan Academy

We are told the pedigree chart represents the inheritance of color blindness through three generations, and we see this here. The standard convention is a square is male, a circle is female. If it's colored in, that means that they exhibit the trait; in this case, it's color blindness. So Bill exhibits color blindness; his phenotype is color blind, while Bonnie does not exhibit color blindness. Color blindness is an X-linked recessive trait.

If Barbara is expecting another child—so this is Barbara right here—what is the probability that it will be color blind? So pause this video and see if you can figure that out on your own.

All right, now let's work through this together. So they're asking us about their next child: what is the probability that it is going to be color blind? To help us with that, we can try to figure out the genotypes of Tom and Barbara. So Tom is pretty straightforward. He is male; we know that because there's a square there.

So, X has an X chromosome and he has a Y chromosome. Color blindness is an X-linked recessive trait, and so let me just make clear what's going on. So I'll do lowercase c for color blind, and I could do a capital C for the dominant trait, which is not color blind. But since they look so similar, I'll just use a plus for not color blind—not color—not color blind.

So Tom, his phenotype, he is color blind, and he only has one X chromosome where the color blind trait is linked to. That must have the recessive allele right over there. So this is Tom's genotype. But what about Barbara? Well, we know Barbara is going to have two X chromosomes because Barbara is female. We know that both of them can't be lowercase c because then Barbara would exhibit color blindness.

But how can we figure out her actual genotype? Well, we could look at her parents. So Bill over here is going to have the same genotype as Tom, at least with respect to color blindness. He is male, so he has an X chromosome and a Y chromosome, and because he exhibits color blindness, that X chromosome must have the recessive color blind allele associated with it.

Now Bonnie, we do not know; she will be XX. She'll have two X chromosomes like Barbara. We know that both of these can't have the recessive allele because then Bonnie would be filled in; she would exhibit color blindness. But we don't know whether she is a carrier or whether she isn't. But let's just think about where Barbara got her chromosomes from. One of her X chromosomes comes from her father, and the other one comes from her mother.

So if she got this X chromosome from her father, her father only has one X chromosome to give, the one that has the color blind allele. So if this is from her father, it must have the color blind allele here. We know that the one from her mother does not have the color blind allele because if it was like this, then Barbara would be color blind, and she isn't. So we know that this must be a plus. Here it is: the dominant non-color blind allele.

So now we know both of their genotypes, and we can use those to then figure out the possible outcomes for their offspring. For example, Tom can contribute an X chromosome that has a color blind allele or a Y chromosome. Barbara, right over here, can contribute an X chromosome that has a color blind allele or an X chromosome that has the non-color blind allele. Barbara is a carrier.

So let me just draw a little Punnett Square here. We have four possible outcomes for their children, and they're all equally likely. So you can get the X chromosome from Barbara that has a color blind allele and the X chromosome from Tom that has the color blind allele. You could have the X chromosome from Barbara with a color blind allele and the Y chromosome from Tom.

You could have the non-color blind X chromosome, or the X chromosome that does not have the color blind allele on it, and get the color blind X chromosome from Tom. Or you could have the non-color blind X chromosome and the Y chromosome from the father. So there are four equal scenarios.

In how many of these scenarios is the offspring color blind? Well, here we have a color blind female; she has two of the recessive alleles, so that female will be color blind. This is a female carrier, but they will not show the phenotype of being color blind. This over here is a color blind male; he has only one X chromosome, and it has the color blind allele on it. This is a non-color blind male.

So out of four equal outcomes, two of them have the offspring being color blind. So two out of four; that would be a 50 probability that the offspring will be color blind.