Interpret independent XX and XY outcomes without a guaranteed family ratio
Equal independent model probabilities give four equally likely ordered outcomes across two conceptions. One of each has probability 50%, but equal small-family counts and alternating outcomes are not guaranteed.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recall the nucleus, DNA base pairing, gametes, fertilisation, enzymes, membrane carriers and chemical synapses.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
After an XX outcome, what is the next XX probability under the stated independent model?
What you will learn
- Distinguish a model probability from a small-sample outcome
- Keep independent conceptions and the stated assumptions
Original teaching model. Counts and records are stipulated; drawings are schematic.
| Feature | Meaning |
|---|---|
| Single model outcome | XX 1/2; XY 1/2 |
| Two ordered outcomes | Four alternatives, each 1/4 |
| One of each | Two alternatives = 1/2 |
| Limit | No guaranteed family ratio or compensating outcome |
Distinguish a model probability from a small-sample outcome
Assume the stipulated XX/XY model supplies X and Y sperm with equal probabilities and fertilisation does not favour either. With an X egg, the probability of XX is one half and the probability of XY is one half. This describes possible outcomes under the assumptions, not a requirement that a small family must contain equal numbers of each combination.
For two independent conceptions, list ordered combinations: XX then XX, XX then XY, XY then XX, and XY then XY. Under the equal-probability assumptions each ordered outcome has probability one quarter. Two XX outcomes therefore have probability one quarter, while one of each in either order has probability one half because two different ordered outcomes count.
Keep independent conceptions and the stated assumptions
Independence means the previous model outcome does not change the probability for the next conception. A run of XX outcomes does not make a Y sperm contribution due next. The tree diagram is a calculation of specified alternatives; it is not a prediction of an actual family’s future chromosome combinations or a personal reproductive forecast.
An original record of ten XX and six XY outcomes need not contradict a half-and-half probability model, because observed small-sample counts can vary. A larger random sample may approach the expected proportions without guaranteeing them exactly. Biological variation beyond the stipulated model remains outside this calculation, and the model does not establish a person’s identity.
Sources for this lesson
Pause and explain
What is the chance of one XX and one XY in either order for two independent model conceptions?
Worked example
Under the model, why is one XX followed by one XY not the only possible two-conception outcome?
Show the worked solution
- List all four ordered outcomes.
- Recognise each independent conception retains both alternatives.
Answer XX/XX, XX/XY, XY/XX and XY/XY are all possible, so a one-of-each pattern is not guaranteed.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
List all ordered XX/XY outcomes for two independent conceptions.
Give me a hint
Each stage has two alternatives.
Compare my reasoning
- Branch first XX into XX and XY.
- Branch first XY into XX and XY.
XX/XX, XX/XY, XY/XX and XY/XY are the four ordered outcomes.
Look for these in your work
- List all four
- Keep order distinct
Calculate the chance of two XX outcomes, and of one XX plus one XY in either order.
Give me a hint
Use four equally likely ordered outcomes.
Compare my reasoning
- Count one outcome for two XX.
- Count two outcomes for one of each.
Two XX: 1/4 or 25%; one of each in either order: 2/4 = 1/2 or 50%.
Look for these in your work
- Use the right outcome counts
- Give correct probabilities
An original record has ten XX and six XY outcomes. Does a half-probability model require the next outcome to be XY?
Give me a hint
Expected proportion is not a compensating rule.
Compare my reasoning
- Recognise sample variation.
- Retain independence for the next outcome.
No. Small-sample counts can vary and do not force a compensating outcome; under the stated independent model the next XX and XY probabilities remain one half each.
Look for these in your work
- Reject forced compensation
- Retain assumptions and independence
Common mistakes
- Equal probability does not guarantee equal small-family counts.
- Previous outcomes do not make the opposite outcome due.
What can you explain now?
What is the chance of one XX and one XY in either order for two independent model conceptions?
Compare with the explanation
One half
Two of four equally likely ordered outcomes count.
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Make it stick
Explain distinguish a model probability from a small-sample outcome and keep independent conceptions and the stated assumptions. Use the stated cell, chromosome sets and information pathway before opening the solutions.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.