# Given the following information, what is the probability that they will have a daughter with hemophilia?

## Hemophilia is caused by several genetic factors; one, a recessive allele of an X-linked gene, is the subject of this problem. Assume that a man with hemophilia marries a normal woman whose father had hemophilia.

50%

#### Explanation:

Let's set up this problem this way:

We're working with the operation of a recessive gene. You may have seen a similar set up for working out the probability of having Brown eyes vs blue eyes (the B in Brown is in caps for being the dominant gene and the b in blue is lower case for being recessive). (NOTE - just like with hemophilia, there are many different causes behind eye colour but in a quick calculation, this works).

The gene for eye colour comes from two sources - Mom and Dad. Mom contributes a gene and Dad contributes the other gene and the result will determine eye colour.

The gene they contribute to the makeup of their child is dependent on their genetic makeup. Both parents either give a B or a b to the child and the result is that the child will have 2 genes and the possibilities are:

BB
Bb
bB
bb

If the child has a B in their genetic makeup, they will have Brown eyes. If they are both b then the child will have blue eyes.

The genetic makeup of the parents is a big determinant as to what is contributed. If someone has blue eyes, that is has a genetic makeup of "bb", they will contribute a b gene. If the parent has Brown eyes, they could have a genetic makeup of BB or Bb. If we know the makeup of the parent, say for instance know for certain they are BB, then we'll know they will throw a B gene. But if they are Bb, it's 50/50 what they'll throw.

Ok - with that background we can tackle the question.

Let's say that the hemophilia gene is marked "h". The gene for no hemophilia is "H" - if the H is present, the child will not have hemophilia.

We know the child gets their genetic makeup from Mom and Dad. What genetic makeups do they have?

Dad is easy - he has hemophilia and so his genetic makeup is "hh". He will contribute an "h" gene.

Mom is normal but her father was a hemophiliac, so we know her genetic makeup is Hh (she is normal so has at least one H in her makeup, but with her dad being a hemophiliac, there is an h from her father in the makeup.)

So it's 50/50 on whether she contributes an H or an h.

So let's run out the possibilities (I've added subscripts to keep track of the genes from each parent):

${H}_{M 1} {h}_{D 1}$
${H}_{M 1} {h}_{D 2}$
${h}_{M 2} {h}_{D 1}$
${h}_{M 2} {h}_{D 2}$

And we have a 50% chance that the child will have hemophilia.