Editing Bayes' theorem (section)

=== Using pedigree to calculate probabilities ===
{| class="wikitable"
!Hypothesis
!Hypothesis 1: Patient is a carrier
!Hypothesis 2: Patient is not a carrier
|-
!Prior Probability
|1/2
|1/2
|-
!Conditional Probability that all four offspring will be unaffected
|(1/2) &sdot; (1/2) &sdot; (1/2) &sdot; (1/2) = 1/16 
|About 1
|-
!Joint Probability
|(1/2) &sdot; (1/16) = 1/32 
|(1/2) &sdot; 1 = 1/2
|-
!Posterior Probability
|(1/32) / (1/32 + 1/2) = 1/17
|(1/2) / (1/32 + 1/2) = 16/17
|}
Example of a Bayesian analysis table for a female's risk for a disease based on the knowledge that the disease is present in her siblings but not in her parents or any of her four children. Based solely on the status of the subject's siblings and parents, she is equally likely to be a carrier as to be a non-carrier (this likelihood is denoted by the Prior Hypothesis). The probability that the subject's four sons would all be unaffected is 1/16 ({{frac|1|2}}&sdot;{{frac|1|2}}&sdot;{{frac|1|2}}&sdot;{{frac|1|2}}) if she is a carrier and about 1 if she is a non-carrier (this is the Conditional Probability). The Joint Probability reconciles these two predictions by multiplying them together. The last line (the Posterior Probability) is calculated by dividing the Joint Probability for each hypothesis by the sum of both joint probabilities.<ref name="Ogino et al 2004">{{cite journal |last1=Ogino |first1=Shuji |last2=Wilson |first2=Robert B |last3=Gold |first3=Bert |last4=Hawley |first4=Pamela |last5=Grody |first5=Wayne W |title=Bayesian analysis for cystic fibrosis risks in prenatal and carrier screening |journal=Genetics in Medicine |date=October 2004 |volume=6 |issue=5 |pages=439–449 |doi=10.1097/01.GIM.0000139511.83336.8F |pmid=15371910 |doi-access=free }}</ref>