Split the cross into one gene at a time, find each fraction, then multiply.
Mendel's rules come down to a coin flip. For each gene, a parent holds two alleles and passes on one at random. Every ratio in this topic — 3:1, 1:1, 9:3:3:1 — is that coin flip, repeated and multiplied.
Key terms
- Allele — one version of a gene. You carry two for each gene, one from each parent.
- Homozygous — two matching alleles, AA or aa. Heterozygous means two different ones, Aa. True-breeding lines are homozygous.
- Dominant — the allele that shows in a heterozygote. The recessive allele is hidden in Aa, not lost, and still gets passed on.
- Genotype — the alleles you carry, like Aa. Phenotype is the trait you show. AA and Aa can look exactly alike.
- Test cross — crossing a dominant-looking individual with a homozygous recessive. The offspring reveal which alleles the unknown carries.
How it works
- In meiosis, homologous chromosomes separate, so each gamete gets one allele of each gene. That's segregation.
- Each homologous pair lines up at metaphase I independently of the others. So genes on different chromosomes sort into gametes independently: independent assortment.
- Fertilization joins one random gamete from each parent. Aa × Aa → 1 AA : 2 Aa : 1 aa, which shows up as 3 dominant : 1 recessive.
- A test cross exposes hidden alleles. Aa × aa → half recessive offspring. AA × aa → none. For genes on different chromosomes, AaBb × aabb → four equal classes.
- For genes on different chromosomes, use the product rule: get each gene's fraction, then multiply. From AaBb × AaBb, aabb = 1/4 × 1/4 = 1/16.
- The same logic counts gamete types. Each heterozygous gene doubles them; homozygous genes add none. AaBBCc → 2 × 1 × 2 = 4.
Why it matters
Mendel's laws are meiosis seen from the outside. Exam questions usually hand you a cross and a table of offspring counts. Your first move is always the same: predict the Mendelian ratio, then compare. A close match supports the model. A clear mismatch is a clue — linked genes, an X-linked gene, or two genes shaping one trait. Chi-square tells you whether a gap is bigger than chance would produce.
Exam traps
| Trap | Actually |
|---|
| The phenotype with more offspring must be the dominant one. | Counts depend on which crosses were made. A phenotype that shows up in offspring but in neither parent is recessive. |
| Two ivory parents gave only ivory offspring, so ivory is dominant. | Recessive parents breed true too: aa × aa gives only aa. A cross with no surprises says nothing about dominance. |
| AaBBCc makes 2 × 2 × 2 = 8 kinds of gametes. | BB always sends B, so only the heterozygous genes double the count: 2 × 1 × 2 = 4. |
| To test a dominant-looking animal, cross it with a true-breeding dominant. | Then every offspring looks dominant either way. Use a homozygous recessive. Any recessive offspring prove a hidden allele. |
Worked example
In an invented herb, purple stems are dominant to green. Two purple-stemmed plants are crossed, and their offspring include 302 purple and 99 green. A breeder picks one purple offspring at random. What is the probability that it carries the green allele?
- Green offspring came from two purple parents, so both parents carry a hidden green allele: Pp × Pp. The 302 : 99 counts fit 3 : 1.
- Pp × Pp gives 1 PP : 2 Pp : 1 pp.
- The breeder already knows the plant is purple, so pp is ruled out. That leaves three equal shares: 1 PP and 2 Pp.
2/3.
Knowing the phenotype shrinks the pool to purple plants only, and two of every three purple plants are Pp. The near miss is 1/2 — that's the share of Pp among all the offspring, green ones included. Always check which group the question is choosing from.