Textbook Question
If two six-sided dice are rolled, what is the probability that the total number of spots showing is
an odd number?
Ch. 2 - Transmission Genetics
Sanders3rd EditionGenetic Analysis: An Integrated ApproachISBN: 9780135564172
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Table of contents
- Ch. 1 - The Molecular Basis of Heredity, Variation, and Evolution64
- Ch. 2 - Transmission Genetics144
- Ch. 3 - Cell Division and Chromosome Heredity81
- Ch. 4 - Gene Interaction87
- Ch. 5 - Genetic Linkage and Mapping in Eukaryotes103
- Ch. 6 - Genetic Analysis and Mapping in Bacteria and Bacteriophages73
- Ch. 7 - DNA Structure and Replication71
- Ch. 8 - Molecular Biology of Transcription and RNA Processing79
- Ch. 9 - The Molecular Biology of Translation110
- Ch. 10 - Eukaryotic Chromosome Abnormalities and Molecular Organization100
- Ch. 11 - Gene Mutation, DNA Repair, and Homologous Recombination86
- Ch. 12 - Regulation of Gene Expression in Bacteria and Bacteriophage90
- Ch. 13 - Regulation of Gene Expression in Eukaryotes38
- Ch. 14 - Analysis of Gene Function via Forward Genetics and Reverse Genetics72
- Ch. 15 - Recombinant DNA Technology and Its Applications69
- Ch. 16 - Genomics: Genetics from a Whole-Genome Perspective49
- Ch. 17 - Organelle Inheritance and the Evolution of Organelle Genomes27
- Ch. 18 - Developmental Genetics43
- Ch. 19 - Genetic Analysis of Quantitative Traits66
- Ch. 20 - Population Genetics and Evolution at the Population, Species, and Molecular Levels105
Sanders3rd EditionGenetic Analysis: An Integrated ApproachISBN: 9780135564172Not the one you use?Change textbook
Chapter 2, Problem 19a
If two six-sided dice are rolled, what is the probability that the total number of spots showing is 4?
Verified step by step guidance1
Identify the total number of possible outcomes when two six-sided dice are rolled. Since each die has 6 faces, the total number of outcomes is 6 × 6 = 36.
Determine the specific outcomes that result in a total of 4. These outcomes are pairs of numbers (x, y) where x + y = 4. For example, (1, 3), (2, 2), and (3, 1).
Count the number of favorable outcomes from the previous step. Ensure that all combinations are included and no duplicates are counted.
Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Use the formula: \( P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \).
Simplify the fraction, if possible, to express the probability in its simplest form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of rolling dice, it quantifies the chance of obtaining a specific outcome, such as a total of 4 spots. The probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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Sample Space
The sample space is the set of all possible outcomes of a random experiment. For rolling two six-sided dice, the sample space consists of all combinations of the two dice, which totals 36 outcomes (6 sides on the first die multiplied by 6 sides on the second die). Understanding the sample space is crucial for calculating probabilities accurately.
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Favorable Outcomes
Favorable outcomes refer to the specific results that satisfy the condition of the probability question. In this case, to find the probability of rolling a total of 4, we need to identify all combinations of the two dice that add up to 4. These combinations are (1,3), (2,2), and (3,1), totaling three favorable outcomes.
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Related Practice
Textbook Question
In pea plants, the appearance of flowers along the main stem is a dominant phenotype called 'axial' and is controlled by an allele T. The recessive phenotype, produced by an allele t, has flowers only at the end of the stem and is called 'terminal.' Pod form displays a dominant phenotype, 'inflated,' controlled by an allele C, and a recessive 'constricted' form, produced by the c allele. A cross is made between a pure-breeding axial, constricted plant and a plant that is pure-breeding terminal, inflated.
Suppose that all of the F₂ progeny with terminal flowers, i.e., plants with terminal flowers and inflated pods and plants with terminal flowers and constricted pods, are saved and allowed to self-fertilize to produce a partial F₃ generation. What is the expected phenotypic distribution among these F₃ plants?
Textbook Question
In pea plants, the appearance of flowers along the main stem is a dominant phenotype called 'axial' and is controlled by an allele T. The recessive phenotype, produced by an allele t, has flowers only at the end of the stem and is called 'terminal.' Pod form displays a dominant phenotype, 'inflated,' controlled by an allele C, and a recessive 'constricted' form, produced by the c allele. A cross is made between a pure-breeding axial, constricted plant and a plant that is pure-breeding terminal, inflated.
If an F₁ plant from the initial cross described above is crossed with a plant that is terminal, constricted, what is the expected distribution among the resulting progeny?
Textbook Question
In pea plants, the appearance of flowers along the main stem is a dominant phenotype called 'axial' and is controlled by an allele T. The recessive phenotype, produced by an allele t, has flowers only at the end of the stem and is called 'terminal.' Pod form displays a dominant phenotype, 'inflated,' controlled by an allele C, and a recessive 'constricted' form, produced by the c allele. A cross is made between a pure-breeding axial, constricted plant and a plant that is pure-breeding terminal, inflated.
If the plants with terminal flowers produced by the cross in part (c) are saved and allowed to self-fertilize, what is the expected phenotypic distribution among the progeny?
Textbook Question
If two six-sided dice are rolled, what is the probability that the total number of spots showing is 7?
Textbook Question
If two six-sided dice are rolled, what is the probability that the total number of spots showing is
greater than 5?
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