By the end of this lesson
- Calculate probabilities from monohybrid crosses.
- Convert among fractions, decimals and percentages.
- Distinguish theoretical probability from observed frequency.
BIG QUESTION
Why can a correct 25% prediction produce no affected children in a small family?
Probability describes repeated independent events, not a quota that nature must fill.
Probability comes from possible gamete combinations
For Aa × Aa, one of four equally likely combinations is aa, so the theoretical probabilityThe chance of an outcome, such as a genetic cross giving a certain phenotype, written as a fraction, ratio, decimal or percentage. is 1/4, 0.25 or 25%.
Always calculate genotype probability before translating it into phenotype.
Independent events do not remember earlier outcomes
If one child has a genotype, the probabilities for a later child are unchanged, assuming parental genotypes and biology are unchanged.
A 25% probability does not mean exactly one in every consecutive group of four children.
Observed frequencies approach expectations in large samples
Random fertilisation causes sampling variation. Small families can differ greatly from expected ratios.
Across many independent offspring, observed proportions often move closer to theoretical probability, though biological factors can also distort ratios.
Probability representations
These forms can express the same prediction.
| Form | Example | Interpretation |
|---|---|---|
| Fraction | 1/4. | One favourable outcome among four equal combinations. |
| Decimal | 0.25. | Probability on a 0–1 scale. |
| Percentage | 25%. | Expected proportion per hundred trials. |
| Ratio | 3:1. | Relative expected counts of two classes. |
| Observed frequency | Data-dependent. | Actual sample outcome. |
Language that earns precision
- probability
- Numerical measure from 0 to 1 of how likely an outcome is.
- independent event
- Event whose outcome does not alter the probability of the next event.
- expected ratio
- Long-run theoretical proportion predicted by a model.
- observed frequency
- Number or proportion actually recorded.
Common misconceptions
Claim: After three unaffected children, the fourth must be affected.
Correction: Each fertilisation is an independent event.
Claim: A Punnett square predicts the exact number in one family.
Correction: It gives theoretical probabilities.
Claim: 25% and 1:3 mean the same ratio notation.
Correction: 25% affected corresponds to affected:unaffected = 1:3.
Match the answer to the command word
Show the cross, count target boxes, then convert units.
Use “probability for each child”, not “every fourth child”.
Recall, apply, then justify
For Aa × aa, calculate the probability of an aa child as a fraction, decimal and percentage.
Hint
Two of four combinations are aa.
Suggested marking points
- The fraction is 1/2.
- The decimal is 0.5.
- The percentage is 50%.
Explain why four children from Aa × Aa need not include exactly one aa child.
Hint
Independent random fertilisation and small samples.
Suggested marking points
- Each fertilisation is an independent random event.
- A small observed sample can differ from the theoretical 1/4 proportion.
Calculate the probability that two successive children from Aa × Aa are both aa, then explain the calculation.
Planning hint
Multiply probabilities for independent events.
What a strong design includes
- The probability of aa for one child is 1/4.
- The two births are treated as independent.
- The joint probability is 1/4 × 1/4.
- This equals 1/16.
- As a decimal it is 0.0625.
- As a percentage it is 6.25%.