# Probability of a genetic disease in the family after 3 generations?

A person can be free from Cystic Fibrosis, a carrier of a single gene, or have two genes. Those with two genes have the condition (let's assume they can't have children, though that's not strictly true).

Carrier frequency is 1 in 25. The probability of a carrier parent passing on their carrier gene is 1 in 2. So the probabilities are as follows:

... Two parents of unknown carrier status having a CF child = 1 in 25 x 1 in 25 x 1 in 2 x 1 in 2 = 1 in 2,500.

... Two parents, one a known carrier and the other of unknown status, having a CF child = 1 x 1 in 25 x 1 in 2 x 1 in 2 = 1 in 100.

... Two parents, both carriers, having a CF child = 1 x 1 x 1 in 2 x 1 in 2 = 1 in 4.

So my question is: what is the respective probability of a carrier and non-carrier having a child with a partner of unknown status that within 3 generations they will have a child with Cystic Fibrosis? Assume two children for each set of parents. The example above is a single generation and single child but I don't trust my summing of probability through the generations and with multiple children.

The genetics is wrong here. The OP's description applies to a recessive disease of a somatic chromosome, but CF is different.

The CF gene is on the X chromosome. Males have only one X chromosome. As you say, in Europe about 1/40 X chromosomes have the disease allele. So about 2/40 women are carriers, and about 1/40 males have the disease at conception.

The reason why we do not see that much CF is most of the affected fetuses die before birth. Until recently, those who survived until birth did not live to child bearing age. So no women suffered from the disease.

However, treatments are now good enough that some affected males could have children. They would pass it on to no sons, but to all of their daughters. They will all be carriers, and an unlucky 1/4o would also inherit the disease from their mother and so suffer from the disease.

(The Y chromosome is short, with few genes, which is why males are the suffers in most genetic diseases of the sex chromosomes.)

I get a 5.96% chance of a carrier having a child in the next 3 generations (2 children, 4 grandchildren, and 8 great-grandchildren). I get 0.32% for a non-carrier, and I get 0.55% for an unknown. I think the unknown stands to reason as 12 random people would be 0.48% (any bad luck not propagated).

Here is my table for a known carrier with an unknown partner, a known non-carrier, and an unknown:

Hopefully the formulas make sense and sorry the image isn't bigger. Note that the generations with *'s utilize the conditional probability for a carrier given no one with CF in that group (actually increases the odds of just being a carrier)