Probability Laws

The sum and product rules of probability are used to determine someone's likelihood of exhibiting a trait.

For example, if an expectant woman's family tree demonstrates a disease, like biotinidase deficiency, her and her partners probability of being carriers of the recessive biotinidase deficiency allele determines their child's risk of having that disorder.

Here, the woman's pedigree shows an afflicted brother but unaffected parents, who must be heterozygous

A punnet square shows the woman could by homozygous for the normal allele or have inherited the disease allele from her mother or father. The homozygous recessive option is discounted. Since there are two ways she could be a carrier, both with probabilities of one in three, the sum of their probabilities is the likelihood she's heterozygous, the sum rule.

Conversely, the father's probability is one in 120, as this is the likelihood a random individual is heterozygous.

Both expectant parents must be carriers, probabilities of two out of three and one out of 120 and pass along the disease allele, a probability of one in four, so the likelihood their child has biotinidase deficiency is the product of these probabilities, approximately 0.14%, the product rule.

This is the calculated theoretical probability yet some couples may only have children with biotinidase deficiency, an observed empirical probability of 100%. However, if many pedigrees were studied, these probabilities would match.