For a single dice roll, there is a 1/6 chance that any particular number will appear. For a pair of dice, each specific combination of numbers has a probability of 1/36 occurring. Most total values of two dice can occur more than one way. As a test of random probability theory, a student decides to roll a pair of six-sided dice 300 times and tabulate the results. She tabulates the number of times each different total value of the two dice occurs. Her results are the following:
Total Value of Two Dice Number of Times Rolled
2 7
3 11
4 23
5 36
6 42
7 53
8 40
9 38
10 30
11 12
12 8
TOTAL 300
The student tells you that her results fail to prove that random chance is the explanation for the outcome of this experiment. Is she correct or incorrect? Support your answer.
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 37d
Textbook Question
Galactosemia is an autosomal recessive disorder caused by the inability to metabolize galactose, a component of the lactose found in mammalian milk. Galactosemia can be partially managed by eliminating dietary intake of lactose and galactose. Amanda is healthy, as are her parents, but her brother Alonzo has galactosemia. Brice has a similar family history. He and his parents are healthy, but his sister Brianna has galactosemia. Amanda and Brice are planning a family and seek genetic counseling. Based on the information provided, complete the following activities and answer the questions.
If the first child has galactosemia, what is the probability that the second child will have galactosemia? Explain the reasoning for your answer.

1
Step 1: Understand the inheritance pattern of galactosemia. Galactosemia is an autosomal recessive disorder, meaning that an individual must inherit two copies of the defective allele (one from each parent) to express the condition. Healthy individuals can be carriers if they have one defective allele and one normal allele.
Step 2: Analyze Amanda and Brice's family history. Both Amanda and Brice are healthy, but each has a sibling with galactosemia. This indicates that Amanda and Brice are likely carriers of the recessive allele, as their parents must have been carriers to produce a child with galactosemia.
Step 3: Determine the probability of Amanda and Brice passing on the recessive allele. Since both Amanda and Brice are carriers, each has a 50% chance of passing on the recessive allele to their child. For a child to have galactosemia, they must inherit the recessive allele from both parents.
Step 4: Calculate the probability of a child having galactosemia. The probability of the first child inheriting the recessive allele from both parents is 0.5 (Amanda's chance) × 0.5 (Brice's chance) = 0.25, or 25%. This probability is independent of whether the first child has galactosemia.
Step 5: Explain why the probability for the second child remains the same. The inheritance of genetic traits follows Mendelian principles, meaning the outcome for one child does not affect the outcome for another. Therefore, the probability that the second child will have galactosemia is also 25%, regardless of whether the first child has the disorder.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Autosomal Recessive Inheritance
Autosomal recessive inheritance occurs when a disorder is expressed only when an individual inherits two copies of a mutated gene, one from each parent. In the case of galactosemia, both parents must be carriers of the recessive allele for their child to be affected. If both parents are healthy but carry the gene, there is a 25% chance with each pregnancy that their child will inherit the disorder.
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Autosomal Pedigrees
Punnett Square
A Punnett square is a diagram used to predict the genetic makeup of offspring from a cross between two parents. It helps visualize the possible combinations of alleles that can result from the parents' genotypes. For autosomal recessive traits, the Punnett square can illustrate the probabilities of having affected (homozygous recessive), carrier (heterozygous), or unaffected (homozygous dominant) children.
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Chi Square Analysis
Probability in Genetics
Probability in genetics refers to the likelihood of inheriting specific traits based on genetic combinations. In the context of galactosemia, if the first child has the disorder, the genetic makeup of the parents remains unchanged, meaning the probability of the second child also having galactosemia is still 25%. This is because each pregnancy is an independent event regarding the inheritance of alleles.
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Probability
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