Probability in Genetics: Examples of the Rule of Multiplication

🧬 Quick Study Guide

• 🧮 The Rule of Multiplication states that the probability of two (or more) independent events occurring together is the product of their individual probabilities.
• 📝 In genetics, independent events often involve the inheritance of different traits.
• 🌱 If the probability of event A is $P(A)$ and the probability of event B is $P(B)$, then the probability of both A and B occurring is: $P(A \text{ and } B) = P(A) \times P(B)$.
• 🔬 For example, if you're crossing two heterozygous individuals ($AaBb$), the probability of an offspring being homozygous recessive for both traits ($aabb$) can be calculated using this rule.
• 🧬 Remember to determine the probability of each event (e.g., getting 'aa' and getting 'bb') separately, then multiply them.
• 💡 This rule assumes independent assortment, meaning the alleles for one trait do not affect the alleles for another.

🧪 Practice Quiz

1. Question 1: If two heterozygous parents ($Aa$) are crossed, what is the probability of their offspring being homozygous recessive ($aa$)?
   1. A) 1/2
   2. B) 1/4
   3. C) 3/4
   4. D) 1
2. Question 2: In guinea pigs, black fur ($B$) is dominant over brown fur ($b$), and short hair ($S$) is dominant over long hair ($s$). If you cross two heterozygous individuals ($BbSs$), what is the probability of an offspring with brown fur and long hair ($bbss$)?
   1. A) 1/2
   2. B) 1/4
   3. C) 1/8
   4. D) 1/16
3. Question 3: A plant with genotype $AaBbCc$ is self-crossed. Assuming independent assortment, what is the probability of an offspring with genotype $AABBCC$?
   1. A) 1/8
   2. B) 1/16
   3. C) 1/64
   4. D) 1/256
4. Question 4: If the probability of a sperm cell carrying allele 'A' is 0.7 and the probability of an egg cell carrying allele 'a' is 0.3, what is the probability of their union resulting in a zygote with genotype 'Aa'?
   1. A) 0.1
   2. B) 0.21
   3. C) 0.42
   4. D) 0.49
5. Question 5: In a dihybrid cross ($AaBb \times AaBb$), what is the probability of an offspring showing the dominant phenotype for both traits, assuming complete dominance?
   1. A) 1/16
   2. B) 3/16
   3. C) 9/16
   4. D) 12/16
6. Question 6: Consider a cross between two individuals with genotypes $AaBbCcDd \times AaBbCcDd$. What is the probability of an offspring having the genotype $aabbccdd$?
   1. A) 1/4
   2. B) 1/16
   3. C) 1/64
   4. D) 1/256
7. Question 7: What is the probability of rolling a 4 on a six-sided die and flipping heads on a fair coin?
   1. A) 1/2
   2. B) 1/4
   3. C) 1/6
   4. D) 1/12