Understand the relationship
The reasoning behind the result
First define one matching outcome
The event might be genotype aa, exact multilocus genotype AaBb, or an expression pattern such as A_bb. The underscore stands only for the second allele in a complete-dominance class. All unspecified biological details remain outside the model.
If a probability comes from another model, enter it directly. Multiplying arbitrary parental probabilities is not a substitute for defining the offspring event.
An exact count includes every ordering
C(n,k) = n! / [k!(n−k)!]
One specific ordering of k matches and n−k nonmatches has probability p^k(1−p)^(n−k). The binomial coefficient counts how many orderings produce that same total. Range probabilities add the mutually exclusive exact-count cases, including both endpoints.
For at least one match, a useful independent check is 1−(1−p)^n. For no matches, use (1−p)^n. These complements are not the probability of exactly one match.
Independence is conditional on known assumptions
The model holds p fixed across offspring and treats outcomes as independent under that p. If parental genotypes are uncertain, the same hidden parental state affects all siblings; averaging p first and using one binomial can be wrong. Analyze each parental scenario separately or use an appropriate joint model.
Expected count np and standard deviation √[np(1−p)] describe the distribution; neither is a promised family outcome or a clinical assessment.
Follow the numbers
Exactly one aa outcome among four offspring
- Aa × Aa gives P(aa)=1/4.
- A specified ordering with one aa and three other outcomes has probability 0.25 × 0.75³ = 0.10546875.
- There are C(4,1)=4 possible positions for the matching offspring.
- Multiply: 4 × 0.10546875 = 0.421875, or 42.1875%.
Exactly one match has probability 42.1875%; at least one has the different probability 1−0.75⁴ = 68.359375%.
Quick guide
How to use this calculator
- Enter a known fixed probability or derive one from two known genotypes and a target pattern.
- Set the number of independent offspring and the inclusive count interval. Use equal endpoints for an exact count.
- Compare the interval probability with the expected count, variability and full count distribution.
Calculation method
Calculation and interpretation
Separate a single-offspring probability from the distribution of counts across independent offspring.
P(K=k) = C(n,k) p^k (1−p)^(n−k); P(L≤K≤U) = sum from k=L to U; E[K]=np.
Worked example
Exactly one aa outcome among four offspring
Exactly one match has probability 42.1875%; at least one has the different probability 1−0.75⁴ = 68.359375%.
P(K=k) = C(n,k) p^k (1−p)^(n−k); P(L≤K≤U) = sum from k=L to U; E[K]=np.
Supported inputs
Precision and limits
Educational inheritance model
Uses a diploid, two-allele model with equal segregation. It does not interpret a person's genetic test, assess disease or reproductive risk, establish parentage, or predict a real offspring's traits. Linkage, selection, incomplete penetrance, mutation, viability differences and environmental effects are excluded.
Fixed independent trials
No family-level uncertainty, shared viability effects or dependence between outcomes is inferred. The full distribution is limited to 1000 offspring; extremely small tails may round below floating-point range.
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