Week 11 — Odds From Coins: The Monohybrid and Dihybrid Report — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Assignment 10 of the term — read a coin-toss model of a cross, predict its counts with the product rule, and explain to a relative why a ratio is odds rather than a promise.

This week you learned Mendel's two laws — each parent passes one allele of each gene, and the alleles of different genes sort independently — and how a Punnett square and the product rule turn a cross into odds. In this assignment you work four short problems, interpret each one, and explain to someone who has never studied biology what a 3:1 ratio does and does not promise. This week's lecture tutorial, quiz, discussion, and Biology Lab & Inquiry practise the same ideas from other angles. It builds on Week 10's meiosis, which is the reason Mendel's two laws hold.

The task

The coin-toss example is an illustrative dataset constructed for this course (not real data). Two coins stand in for two Tt parents: heads stands for T, the dominant allele, and tails for t, the recessive allele. Flipping both coins makes one offspring. In 100 two-coin flips the run gave:

• 23 TT offspring;
• 52 Tt offspring;
• 25 tt offspring.

Work these four problems, showing your arithmetic:

1. In the coin-toss example (illustrative), 100 two-coin flips gave 23 TT and 52 Tt offspring. How many offspring show the dominant trait?
2. Each Tt parent passes t with probability 1⁄2, so P(tt) = 1⁄2 × 1⁄2 = 1⁄4. How many tt offspring do the odds predict in 100 two-coin flips?
3. In the dihybrid cross TtYy × TtYy, each gene alone gives the dominant trait with probability 3⁄4, and the grid has 16 boxes. How many of the 16 boxes show both dominant traits?
4. In the coin-toss example (illustrative), 75 offspring show the dominant trait and 25 show the recessive trait. How many dominant offspring are there for every one recessive offspring?

Beside each answer, add one brief interpretation:

• Problem 1: explain why TT and Tt both count as showing the dominant trait, and keep the genotype ratio you would predict for Tt × Tt separate from the phenotype ratio.
• Problem 2: name the probability rule that gives P(tt), and explain through the law of segregation why each parent passes only one allele, naming the division of meiosis where the alleles separate.
• Problem 3: name the four gamete types a TtYy parent makes, and explain the law of independent assortment in terms of what chromosome pairs do in meiosis I.
• Problem 4: compare the run with the counts the odds predict, and explain why a real run lands near the prediction rather than exactly on it and what more flips would do.

Explain it to a non-expert

A relative who keeps rabbits as a hobby asks, "If both of my rabbits carry the hidden allele for a recessive coat, will exactly one of the next four babies show it?" The rabbits and their coat trait are made up for this assignment. Write a 3–5 sentence message that explains, in everyday words, what a 3:1 ratio does and does not promise for a litter of four, connects it to your coin-toss run, and names one limit, including that your coin numbers are illustrative rather than measured. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a friend asking why salted lettuce goes limp. Model answer: "Lettuce leaves are made of cells, and each cell is wrapped in a thin skin that lets water pass. Water tends to move toward the side with more dissolved stuff, so when salt coats the outside of the leaf, water leaves the cells. With less water inside, the cells sag and the leaf wilts. This explains the wilting, but it does not tell you exactly how long it takes, which depends on how much salt you use."

Use that pattern for your relative's rabbits, with your own wording and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the counts and probabilities in the problems without guessing which values or steps you used.

Deliverables

Submit a single report containing:

• the four answers, each with the arithmetic shown and the brief interpretation the task names for that problem;
• your message to your relative, explaining in everyday words what a 3:1 ratio does and does not promise for a litter of four, with one limit; and
• a one-line restatement of the coin-toss counts you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled hand-drawn Punnett square with a short note. Every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the arithmetic, the interpretations, and the writing yourself, without a chatbot or other AI tool. You may use a calculator, a spreadsheet, or two real coins. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

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