10. Patterns of Inheritance


10.3. Probability vs. Possibility


Your ability to understand genetics depends on your ability to work with probabilities. This section will help you understand what probability is.

Probability is the mathematical chance that an event will happen, and it is expressed as a percentage or a fraction, like the values that we identified using the Punnett square in the previous example. Probability is not the same as possibility. Consider the common phrase “almost anything is possible” when reading the following question: “It is possible for me to win the lottery, but how probable is it?” Although it is possible to win the lottery, it is extremely unlikely. When we talk about something being probable, we actually talk mathematically— in ratios and percentages—such as, “The probability of my winning the lottery is 1 in 250,000.”

It is possible to toss a coin and have it come up heads, but the probability of getting a head is a more precise statement than just saying it is possible to do so. The probability of getting a head is 1 out of 2 (1/2, or 0.5, or 50%), because there are two sides to the coin, only one of which is a head. Probability can be expressed as a fraction:

What is the probability of cutting a standard deck of cards and getting the ace of hearts? The number of times the ace of hearts can occur in a standard deck is 1. The total number of different cards in the deck is 52. Therefore, the probability of cutting to an ace of hearts is 1/52. What is the probability of cutting to any ace? The total number of aces in the deck is 4, and the total number of cards is 52. Therefore, the probability of cutting an ace is 4/52, or 1/13.




It is also possible to determine the probability of two independent events occurring together. The probability of two or more events occurring simultaneously is the product of their individual probabilities. When two six-sided dice are thrown, it is possible that both will be 4s. What is the probability that both will be 4s? The probability of one die being a 4 is one out of the six sides of the die, or 1/6. The probability of the other die being a 4 is also 1/6. Therefore, the probability of throwing two 4s is

1/6 x 1/6 = 1/36

The concepts of probability and possibility are frequently used in solving genetics problems (How Science Works 10.1). Consider describing the genetic contents of the sex cells an individual will produce. Assume that the individual’s genotype is AA. It is only possible for this individual to produce sex cells that carry the A allele. The probability of this occurring is 100%. Now consider an individual with the Aa genotype.

It is possible for the Aa individual to produce A or a sex cells. The probability of a sex cell having A is 50%; only one of the two possibilities is A. Likewise, the probability of a sex cell having a is 50%; only one of the two possibilities is a.

In a genetics problem, the frequency with which alleles are present in gametes determines the likelihood that a couple will have children with a particular characteristic. Consider the possible fertilization events that could occur between an individual with the genotype AA and an individual with the genotype aa (the genetic cross AA x aa). To do this, use a Punnett square. First, predict the possible sex cells produced by each individual.

Then, set up a Punnett square that shows the possible fertilization events between the sex cells shown.

The only possible offspring is Aa. The probability of obtaining an offspring with this genotype is 100%.



Cystic Fibrosis—What Is the Probability?

Cystic fibrosis is among the most common lethal genetic disorders that affect Caucasians. An estimated 30,000 people are affected by cystic fibrosis in North America. One in every 20 persons has a defective recessive allele that causes cystic fibrosis, but most of these individuals display no cystic fibrosis symptoms, because they are heterozygous and the recessive allele is masked by a normal dominant allele. Only those with two copies of the defective recessive gene develop symptoms. About 1,000 new cystic fibrosis cases are identified in the United States each year. The gene for cystic fibrosis occurs on chromosome 7; it is responsible for the manufacture of cystic fibrosis transmembrane regulator (CFTR) protein. The CFTR protein controls the movement of chloride ions across the cell membrane.

There are many possible types of mutations in the CFTR gene. The most common mutation results in a CFTR protein with a deletion of a single amino acid. As a result, CFTR protein is unable to control the movement of chloride ions across the cell membrane. The major result is mucus filling the bronchioles, resulting in blocked breathing and frequent respiratory infections. It is also responsible for other symptoms:

1. A malfunction of sweat glands in the skin and the secretion of excess chloride ions

2. Clogging of the bile duct, which interferes with digestion and liver function

3. Mucus clogging the pancreas ducts, preventing the flow of digestive enzymes into the intestinal tract

4. Bowel obstructions caused by thickened stools

5. Sterility in males that is due to the absence of vas deferens and, on occasion, female sterility due to the presence of dense mucus-blocking sperm from reaching eggs.




One in 20 people have a recessive allele for cystic fibrosis. In this group, two or three individuals, on average, have the allele.


Consider the facts about the frequency of the cystic fibrosis gene in the population. What is the probability that any set of parents will have a child with cystic fibrosis? What is the probability that a person who carries the cystic fibrosis allele will marry someone who also has the allele?



8. What is the difference between probability and possibility?

9. In what mathematical forms might probability be expressed?