Probability

A Punnett square uses probability to explain what sorts of children two parents might have. Suppose a couple knows that cystic fibrosis, a debilitating respiratory disease, tends to run in the man's family. The couple would like to know how likely it is that they would pass on the disease to their children.

A clinical geneticist can use a Punnett square to help answer the couple's question. The clinical geneticist might start by explaining how the disease is inherited: Because cystic fibrosis is a recessive disease caused by a single gene, only children who inherit the disease-causing form of the cystic fibrosis gene from both parents display symptoms. On the other hand, because the cystic fibrosis gene is a recessive gene, a child who inherits only Both parents are carriers of the recessive CF gene(f) in this Punnett square. The probability of having a child with CF, if both parents are carriers, is 25 percent. one copy of a defective gene, along with one normal version, will not have the disease.

Suppose the recessive, disease-causing form of the gene is referred to as "f" and the normal form of the gene is referred to as "F." Only individuals with two disease-causing genes, ff, would have the disease. Individuals with either two normal copies of the gene (FF) or one normal copy and one mutated copy (Ff) would be healthy.

If the clinical geneticist tests the parents and finds that each carries one copy of the cystic fibrosis gene, f, and one copy of the normal gene, F, what would be the probability that a baby of theirs would be born with the cystic fibrosis disease? To answer this question, we can use the Punnett square shown in the figure above. A Punnett square assumes that there is an equal probability that the parent will pass on either of its two gene forms ("alleles") to each child.

The parents' genes are represented along the edges of the square. A child inherits one gene from its mother and one from its father. The combinations of genes that the child of two Ff parents could inherit are represented by the boxes inside the square.

Of the four combinations possible, three involve the child's inheriting at least one copy of the dominant, healthy gene. In three of the four combinations, therefore, the child would not have cystic fibrosis. In only one of the four combinations would the child inherit the recessive allele from both parents. In that case, the child would have the disease. Based on the Punnett square, the counselor can tell the parents that there is a 25 percent probability, or a one-in-four chance, that their baby will have cystic fibrosis.