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 19b
If two six-sided dice are rolled, what is the probability that the total number of spots showing is 7?
Verified step by step guidance1
Understand the problem: You are rolling two six-sided dice, and you need to calculate the probability that the sum of the numbers on the two dice equals 7.
Determine the total number of possible outcomes: Each die has 6 faces, so the total number of outcomes when rolling two dice is 6 × 6 = 36.
Identify the favorable outcomes: List all the pairs of numbers on the two dice that add up to 7. These pairs are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 favorable outcomes.
Calculate the probability: The probability of an event is given by the formula: . Substitute the values: .
Simplify the fraction 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 the sum of the numbers showing on the dice. The probability of an event 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 pairs of numbers that can appear, ranging from (1,1) to (6,6). This results in a total of 36 possible outcomes, which is crucial for calculating probabilities related to specific sums, such as 7.
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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 7 with two dice, we identify all combinations that yield this sum, such as (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are six favorable outcomes, which are essential for calculating the probability.
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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.
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 4?
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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Textbook Question
Experimental Insight 2.1 describes data, collected by a genetics class like yours, on the numbers of kernels of different colors in bicolor corn. To test the hypothesis that the presence of kernels of different colors in each ear is the result of the segregation of two alleles of a single gene, the class counted 12,356 kernels and found that 9304 were yellow and 3052 were white. Use chi-square analysis to evaluate the fit between the segregation hypothesis and the class results.