Rucete ✏ Campbell Biology In a Nutshell
Unit 3 GENETICS — Concept 14.2 Probability Laws Govern Mendelian Inheritance
Mendel’s laws of inheritance follow the same probability rules used in everyday events like flipping coins or drawing cards. These rules allow us to predict the likelihood of specific genotypes and phenotypes in offspring.
Probability and Inheritance
- The laws of segregation and independent assortment reflect basic rules of probability
- The chance of an event is a number between 0 (impossible) and 1 (certain)
- The sum of all possible outcomes' probabilities must equal 1
- Past events (e.g., prior coin tosses) do not influence future outcomes—each is independent
Multiplication Rule
- To determine the chance of two or more independent events happening together, multiply their probabilities
- Example: Probability of getting heads on two coins = ½ × ½ = ¼
- Example: Probability of an F₂ pea plant being rr (wrinkled seeds) = ½ (r from egg) × ½ (r from sperm) = ¼
Addition Rule
- For mutually exclusive events, add their individual probabilities
- Example: Probability of an F₂ plant being heterozygous (Rr) =
- R from egg and r from sperm (¼)
- or r from egg and R from sperm (¼)
- Total = ¼ + ¼ = ½
Solving Complex Crosses with Probability
- Dihybrid and trihybrid crosses can be solved by combining simple monohybrid probabilities
- For a dihybrid cross (YyRr × YyRr):
- Probability of YY = ¼, of RR = ¼ → YYRR = ¼ × ¼ = 1⁄16
- YyRR = ½ × ¼ = 1⁄8
- For more complex problems (e.g., three traits), use multiplication for each gene’s outcome and addition to sum combinations that satisfy a condition
- Example: Calculating the fraction of offspring showing at least two recessive traits involves identifying all matching genotypes, finding each probability, and summing them
- These probability rules allow for faster predictions than creating large Punnett squares
In a Nutshell
The outcomes of genetic crosses can be predicted using the multiplication and addition rules of probability. These rules reflect the random behavior of allele segregation and fertilization, forming the mathematical basis of Mendelian genetics.