A couple with European ancestry seeks genetic counseling before having children because of a history of cystic fibrosis (CF) in the husband's family. ASO testing for CF reveals that the husband is heterozygous for the Δ508 mutation and that the wife is heterozygous for the R117 mutation. You are the couple's genetic counselor. When consulting with you, they express their conviction that they are not at risk for having an affected child because they each carry different mutations and cannot have a child who is homozygous for either mutation. What would you say to them?
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 8b
Textbook Question
Determine whether the statements below are true or false. If a statement is false, provide the correct information or revise the statement to make it correct.
A student uses the product rule to predict that the probability of flipping a coin twice and getting a head and then a tail is 1/4.

1
Understand the problem: The student is using the product rule to calculate the probability of flipping a coin twice and getting a head followed by a tail. The product rule states that the probability of two independent events occurring together is the product of their individual probabilities.
Define the probabilities: For a fair coin, the probability of flipping a head (H) is 1/2, and the probability of flipping a tail (T) is also 1/2. These events are independent, meaning the outcome of the first flip does not affect the outcome of the second flip.
Apply the product rule: Multiply the probability of flipping a head (1/2) by the probability of flipping a tail (1/2). This gives the probability of flipping a head followed by a tail.
Verify the student's calculation: The student predicted the probability to be 1/4. Check if this matches the result obtained using the product rule.
Evaluate the statement: Determine whether the statement is true or false based on the calculation. If false, revise the statement to clarify the correct probability and reasoning.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Product Rule in Probability
The product rule in probability states that the probability of two independent events occurring together is the product of their individual probabilities. For example, if the probability of flipping a head on a coin is 1/2 and the probability of flipping a tail is also 1/2, the probability of both events occurring in sequence (head followed by tail) is 1/2 * 1/2 = 1/4.
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Independent Events
Independent events are those whose outcomes do not affect each other. In the context of coin flips, the result of the first flip does not influence the result of the second flip. This independence is crucial for applying the product rule correctly, as it allows us to multiply the probabilities of each event.
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Probability of Coin Flips
When flipping a fair coin, the probability of landing on heads or tails is equal, each being 1/2. Therefore, when calculating the probability of a specific sequence of flips, such as getting a head followed by a tail, one must consider the individual probabilities of each flip and apply the product rule to find the overall probability.
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