If two six-sided dice are rolled, what is the probability that the total number of spots showing is 4?
Table of contents
- 1. Introduction to Genetics51m
- 2. Mendel's Laws of Inheritance3h 37m
- 3. Extensions to Mendelian Inheritance2h 41m
- 4. Genetic Mapping and Linkage2h 28m
- 5. Genetics of Bacteria and Viruses1h 21m
- 6. Chromosomal Variation1h 48m
- 7. DNA and Chromosome Structure56m
- 8. DNA Replication1h 10m
- 9. Mitosis and Meiosis1h 34m
- 10. Transcription1h 0m
- 11. Translation58m
- 12. Gene Regulation in Prokaryotes1h 19m
- 13. Gene Regulation in Eukaryotes44m
- 14. Genetic Control of Development44m
- 15. Genomes and Genomics1h 50m
- 16. Transposable Elements47m
- 17. Mutation, Repair, and Recombination1h 6m
- 18. Molecular Genetic Tools19m
- 19. Cancer Genetics29m
- 20. Quantitative Genetics1h 26m
- 21. Population Genetics50m
- 22. Evolutionary Genetics29m
2. Mendel's Laws of Inheritance
Probability and Genetics
Problem 20a
Textbook Question
In a plant, a tall variety was crossed with a dwarf variety. All F₁ plants were tall. When F₁xF₁ plants were interbred, 9/16 of the F₂ were tall and 7/16 were dwarf. Explain the inheritance of height by indicating the number of gene pairs involved and by designating which genotypes yield tall and which yield dwarf. (Use dashes where appropriate.)

1
Step 1: Recognize that the inheritance pattern suggests a dihybrid cross, as the phenotypic ratio (9:7) deviates from the classic Mendelian monohybrid ratio (3:1). This indicates that two gene pairs are involved in determining plant height.
Step 2: Assign symbols to the alleles. Let 'A' and 'B' represent dominant alleles for height, and 'a' and 'b' represent recessive alleles. The tall phenotype requires at least one dominant allele from each gene pair (A-B-), while the dwarf phenotype occurs when either gene pair is homozygous recessive (aa-- or --bb).
Step 3: Write the genotypes for the F₁ generation. Since all F₁ plants are tall, they must be heterozygous for both gene pairs (AaBb). This ensures that they carry one dominant allele for each gene pair, resulting in the tall phenotype.
Step 4: Perform a Punnett square for the F₁ x F₁ cross (AaBb x AaBb). This involves combining the alleles from each parent to determine the genotypes of the F₂ generation. The possible genotypes are: AABB, AABb, AaBB, AaBb, AAbb, Aabb, aaBB, aaBb, and aabb.
Step 5: Determine the phenotypes of the F₂ generation based on the genotypes. The tall phenotype (A-B-) includes genotypes with at least one dominant allele for each gene pair (AABB, AABb, AaBB, AaBb), which accounts for 9/16 of the offspring. The dwarf phenotype includes genotypes with homozygous recessive alleles for at least one gene pair (AAbb, Aabb, aaBB, aaBb, aabb), which accounts for 7/16 of the offspring.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mendelian Inheritance
Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which include the concepts of dominant and recessive traits. In this case, the tall variety is dominant over the dwarf variety, meaning that the presence of at least one dominant allele results in a tall phenotype. This principle helps explain the observed phenotypic ratios in the offspring.
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Gene Pairs and Alleles
In this scenario, height in plants is determined by a pair of alleles, where one allele is dominant (T for tall) and the other is recessive (t for dwarf). The genotypes can be TT (homozygous tall), Tt (heterozygous tall), or tt (homozygous dwarf). The combination of these alleles during reproduction leads to the phenotypic ratios observed in the F₂ generation.
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Phenotypic Ratios
Phenotypic ratios describe the relative frequencies of different phenotypes in the offspring resulting from a genetic cross. In this case, the F₂ generation exhibits a 9:7 ratio of tall to dwarf plants, indicating that 9 out of 16 plants are tall (TT or Tt) and 7 out of 16 are dwarf (tt). This ratio reflects the inheritance pattern and the interaction of the alleles involved.
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