Examples of the Product Rule in Heredity

📚 Quick Study Guide

• 🧬 The product rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.
• 🧮 Mathematically, if events A and B are independent, then the probability of both A AND B occurring is: $P(A \text{ and } B) = P(A) \times P(B)$
• 🌱 In heredity, independent events often refer to the inheritance of different traits (assuming no gene linkage).
• 💡 Key Idea: Determine the probability of each individual event (trait) separately, then multiply them to get the combined probability.
• 📝 Example: If the probability of a plant having red flowers is $\frac{1}{2}$ and the probability of it having tall stems is $\frac{3}{4}$, then the probability of it having BOTH red flowers AND tall stems is $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$.

🧪 Practice Quiz

1. A plant can have purple (P) or white (p) flowers and round (R) or wrinkled (r) seeds. If a plant is heterozygous for both traits (PpRr), and these traits assort independently, what is the probability that its offspring will have purple flowers and round seeds?
   1. $\frac{1}{16}$
   2. $\frac{3}{16}$
   3. $\frac{9}{16}$
   4. $\frac{1}{4}$


2. In guinea pigs, black fur (B) is dominant to brown fur (b), and rough fur (R) is dominant to smooth fur (r). If you cross a guinea pig that is heterozygous for both traits (BbRr), what is the probability that its offspring will have black, smooth fur?
   1. $\frac{1}{16}$
   2. $\frac{3}{16}$
   3. $\frac{9}{16}$
   4. $\frac{1}{4}$


3. A couple, both with the genotype AaBb, are planning to have a child. Assuming that the A and B genes assort independently, what is the probability that their child will have the genotype AABB?
   1. $\frac{1}{2}$
   2. $\frac{1}{4}$
   3. $\frac{1}{8}$
   4. $\frac{1}{16}$


4. If two genes, A and B, are located on different chromosomes, and the probability of inheriting allele A is 0.25 and the probability of inheriting allele B is 0.5, what is the probability of inheriting both A and B?
   1. 0.125
   2. 0.25
   3. 0.5
   4. 0.75


5. In a certain species of bird, long beaks (L) are dominant to short beaks (l), and brown feathers (B) are dominant to white feathers (b). If two birds heterozygous for both traits (LlBb) mate, what is the probability that their offspring will have long beaks and white feathers?
   1. $\frac{1}{16}$
   2. $\frac{3}{16}$
   3. $\frac{9}{16}$
   4. $\frac{1}{4}$


6. Assume gene A (alleles A and a) and gene B (alleles B and b) are unlinked. An individual with genotype AaBb is crossed with an individual with genotype aabb. What proportion of the offspring will have the genotype aaBb?
   1. $\frac{1}{2}$
   2. $\frac{1}{4}$
   3. $\frac{1}{8}$
   4. $\frac{1}{16}$


7. In pea plants, yellow seeds (Y) are dominant to green seeds (y), and inflated pods (I) are dominant to constricted pods (i). If a plant heterozygous for both traits (YyIi) is allowed to self-fertilize, what proportion of the offspring will have yellow seeds and constricted pods?
   1. $\frac{1}{16}$
   2. $\frac{3}{16}$
   3. $\frac{9}{16}$
   4. $\frac{1}{4}$