### Description

Bayes theorem can be used to adjust the risk of being a carrier for a genetic condition if additional modifying information is available.

 Carrier Noncarrier prior probability (risk) 1 - (risk) conditional probability (conditional risk carrier) (conditional risk noncarrier) joint risk (risk) * (conditional risk carrier) (1 - (risk)) * (conditional risk noncarrier)

where:

• The prior probability for being a carrier in many genetic conditions if one parent is a known carrier is 0.5.

• The conditional probability for being a noncarrier is 1 if offspring are normal.

posterior probability of being a carrier =

= ((risk) * (conditional risk carrier)) / (((risk) * (conditional risk carrier)) + ((1 - (risk)) * (conditional risk noncarrier)))

posterior probability of being a noncarrier =

= ((1 - (risk))* (conditional risk noncarrier)) / (((risk) * (conditional risk carrier)) + ((1 - (risk)) * (conditional risk noncarrier)))

For the situation where previous offspring are all normal (conditional risk for noncarrier = 1):

posterior probability of being a carrier =

= ((risk) * (conditional risk carrier)) / (((risk) * (conditional risk carrier)) + (1 - (risk))) =

= ((risk) * (conditional risk carrier)) / (((risk) * ((conditional risk carrier) - 1)) + 1)

posterior probability of being a noncarrier =

= (1 - (risk)) / (((risk) * (conditional risk carrier)) + (1 - (risk))) =

= 1 - (posterior risk of being a carrier)