K327 / K328 / 2027

Lesson 6 of 9 / Inheritance

Expected ratios are probabilities

Why might five offspring fail to match a 3:1 prediction?

I can explain chance differences between expected and observed inheritance ratios, especially in small samples.

  • I can explain observed deviations from expected ratios, particularly in small samples.Syllabus

    Syllabus K327 / K328, Topic 12(e). Explain observed deviations from expected ratios, particularly in small samples.

About 5 min

Make a guess. You are not marked.

Two carriers (Rr x Rr) have three children who all show the dominant trait. What is the chance their fourth child shows the recessive trait?

  1. Zero, because the pattern shows they cannot.
  2. Certain, to complete the 3:1 ratio.
  3. 1/4, the same as for every child.
Show the answer

1/4, the same as for every child.

Each fertilisation is a fresh chance. Earlier children do not change the odds for the next one.

The key idea

Random gamete combinations can make an observed ratio differ from its expected probability. Small samples show larger proportional fluctuations.

Does a small sample have to match the prediction?

Both illustrative samples use Rr x Rr with an expected 3 round : 1 wrinkled ratio.

Expected75%25%Observed75Same total bar length = 100%
Counts in the selected illustrative sample
PhenotypeExpectedObserved
Round97
Wrinkled35

Green: round. Gold: wrinkled. Bar widths show proportions, and the table gives counts. These are fixed illustrative datasets, not a random biological simulation.

Explanation

A Punnett square lists possible allele combinations and their probabilities under a model. It does not predict the order of births or require a family to contain every box exactly once. Each fertilisation combines gametes as a separate chance event.

For Rr x Rr, a recessive offspring has probability 1/4 each time under the model. If the first three offspring show the dominant phenotype, the fourth still has probability 1/4 of being recessive. The earlier outcomes do not use up dominant combinations or force a recessive one next.

In a small sample, one additional offspring makes a large difference to the observed proportion. Larger samples usually give proportions closer to the expected probabilities, although an exact ratio is still not guaranteed.

Report observations separately from expectations. For example, 5 recessive offspring among 12 gives an observed recessive proportion of 5/12, about 42%, while the model expects 25%. This difference alone in a small sample does not show the inheritance model is wrong. Repeated large, systematic differences would need further investigation.

Step by step
  1. 1

    Calculate the expectation

    Use the cross to find the probability, then multiply by the sample size.

  2. 2

    State the observation

    Use the actual counts and avoid relabelling them as predictions.

  3. 3

    Explain the difference

    Random gamete combinations and a small sample can produce chance deviations.

Worked example

Twelve offspring

Rr x Rr produces 7 round and 5 wrinkled offspring. State the expected numbers and explain the difference.

One way to explain it

The expectation is 12 x 3/4 = 9 round and 12 x 1/4 = 3 wrinkled. The observed 7:5 ratio differs because random fertilisation in a small sample can produce chance fluctuations.

Why this answer works
  • Expected and observed counts are different kinds of information.
  • The total remains 12 in both comparisons.
  • Do not change the probability of the next offspring to compensate.

Watch out for this

A student says: "After three dominant offspring, the next one must be recessive to complete 3:1." What is wrong with this?

Show the answer

The model gives the same probability at each fertilisation. Previous outcomes do not force the next outcome.

Check your understanding

For Rr x Rr, the first three offspring are round. What is the probability that the next is wrinkled?

  1. 0, because the parents can make only round offspring
  2. 1/4 under the same inheritance model
  3. 1, because the ratio must now be completed
Show the answer

1/4 under the same inheritance model

A fresh random combination of gametes has the same probability regardless of the earlier results.

Exam-style questions

Check your understanding

A cross of two heterozygous tall pea plants gives 316 tall and 104 short offspring. Which conclusion is best?

  1. The result is close to the expected 3 : 1 ratio
  2. The result proves that tall is recessive to short
  3. The result is far from 3 : 1, so the model must be wrong
  4. The result is a 1 : 1 ratio, so one parent was homozygous
Show the answer

The result is close to the expected 3 : 1 ratio

316 : 104 is about 3.04 : 1, which is close to 3 : 1; random fertilisation explains the small difference.

Quick recall

Card 1 of 3. Answer in your head, then check.

Why might five offspring fail to match a 3:1 prediction?

You can return to this lesson any time.