Biology 11–12 · Year 12

Coin-toss crosses: predicted ratios, sampling scatter and the chi-squared test

Module 5: Heredity (Genetic Variation)

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The idea

A Punnett square predicts a ratio, but real offspring counts scatter around it, and a chi-squared test decides whether the scatter is more than chance.

What you need

Two coins per pair, one marked A on one face and a on the other for each parent (a heterozygous cross)
Recording sheet; calculator or spreadsheet; the NIST chi-squared critical value table

How to do it

Draw the Punnett square for Aa x Aa and write the expected genotype ratio 1 AA : 2 Aa : 1 aa and phenotype ratio 3 dominant : 1 recessive.
Toss both coins 40 times, recording each pair as AA, Aa or aa; tally the phenotypes.
Pool the class results to a few hundred offspring.
For your own 40 and for the class pool, compute chi-squared = sum over classes of (observed minus expected)^2 / expected for the 3 : 1 phenotype split, and compare with the critical value 3.841 (one degree of freedom, 0.05 level).
Repeat for a dihybrid cross with four coins and the 9 : 3 : 3 : 1 expectation (three degrees of freedom, critical value 7.815).
Explain why the class pool sits closer to the predicted ratio than most individual sets.

What you should see

Individual sets of 40 tosses scatter: a result of 28 dominant to 12 recessive gives chi-squared 0.53 and is consistent with 3 : 1, while the class pool settles near 75 percent dominant. A count of 70 dominant and 30 recessive in 100 gives chi-squared 1.33, below 3.841, so the deviation from 3 : 1 is not significant (computed). The learner knows it worked when the pooled proportion is closer to 0.75 than most single sets and the chi-squared values fall below the critical value in nearly every set.

What changes

What you change: sample size (40 versus the class pool)
What you measure: deviation of the observed ratio from the predicted ratio, and chi-squared
What you keep the same: fair coins
recording rule
cross type

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A 3 : 1 ratio means every four offspring include exactly one recessive; the ratio is a probability, not a rule for each family.
A result that differs from the prediction proves the model wrong; small samples differ by chance, and the test measures that.
Dominant alleles are more common in a population; dominance is about expression, not frequency.

Safety card

Low riskLearners carry it out

Hazards

No hazard is listed.

Controls

No control is listed.

Note

No hazards.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Biology Stage 6 Syllabus (2017), current: Year 11 taught to the end of 2026 and Year 12 to Term 3 2027BIO12-12 BIO11/12-4 BIO11/12-5
Biology 11–12 Syllabus (2025), Year 12 focus area Heredity; new syllabus not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027BI-12-01
Biology 11–12 Syllabus (2025), Year 12 Working scientifically; new syllabus not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027BI-12WS-04 BI-12WS-05
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

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