Jane and Peter have two healthy children but Jane’s sister has a child recently diagnosed with CF. Peter has no family history of CF. What is the chance that Jane and Peter’s next child will have CF? Both of them are of Caucasian ancestry.
|
|
Carrier |
Non-carrier |
|
Prior |
2/3 |
1/3 |
|
Conditional |
1/4 x 1/4 x 1/4 = 1/64 |
1 |
|
Joint |
1/96 |
1/3 |
|
Posterior |
1/96 / (1/96 + 1/3) = 1/33 |
1/3 / (1/96 + 1/3) = 32/33 |
The probability that Jane is a carrier of the cystic fibrosis gene is 1/33
The probability that Peter is a carrier of the cystic fibrosis gene, based solely on his ethnicity/ancestry (due to negative family history of CF) is 1/25
We multiply these probabilities to get:
1/33 x 1/25 = 1/825 (the probability that their third child will have cystic fibrosis)