Sickle Probability

A peep into My Patients' Files took me to Sickle Cell Disease (SCDx).

SCDx is a blood disorder in which the Red Blood Cells (RBC) loose their discoid shape and become sickle-shaped thus losing their ability to transport oxygen and also blocking arteries thereby preventing blood flow to the organs. Sufferers of the disease are commonly referred to as "sicklers"  or "SS". They possess the genotype SS. Normal individuals are AA while AS is the carrier state. They suffer agonizing pains known as "crisis" leading to frequent and recurrent visits to the hospital.

My patient is a 29 year old woman and she already has her 4th child. Lucky woman you are, I teased. At 29, four kids already.

Not that lucky she replied. My first child, a boy is AA, the second, a girl is AS while the third is SS. This 3 month old I'm carrying, only time will tell what his genotype is.

The third child had been falling ill frequently and it was discovered that she suffered from SCDx. It was at that time that the couple also realized they were both carriers, AS-AS. They had no pre-marriage testing.

I had many questions on my mind for her like, "would you have married him if you knew from the outset that you were both carriers?"how did you feel knowing you have given birth to a sickler?" but I asked her only one - Why did you go ahead to having a fourth child after discovering that your third child is a sickler? I would have expected that you'd stop child bearing after three kids. Is it an automated natural compulsion to procreate or have you calculated the probability and found out that the fourth cannot be sickler?

As the full effects of the symptoms manifest as the child grows older, I wonder how it will impact on the whole family and how they would handle it. 

The truth is this, the occurrence of SCDx actually lies only in the hands of God. There are families who had no sicklers, while there are others who had multiple. However, the choice "to" or "not to" take the risk lies in our own hands.

This peculiar case got me calculating probabilities. I disliked the topic back in secondary school. Circle geometry was my favorite. Just curious, for you math gurus, what is the probability that (a) the fourth child would be a sickler and (b) what is the probability that he would not?