Does a monohybrid cross always give exactly 3 dominant : 1 recessive?
Short answer: 3:1 is a probability for each child. With only 4 children, other ratios happen often (exactly 3:1 has probability about 42%).
The trap
The wrong idea
“A monohybrid cross with 4 offspring will give exactly 3 dominant : 1 recessive.”
It sounds reasonable, and a lot of NEET aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
Two Aa parents have 4 children. Exactly 3 dominant and 1 recessive is:
- Certain
- Likely but not certain
- Impossible
Show the answer
B. Likely but not certain
3:1 is a probability for each child. With only 4 children, other ratios happen often (exactly 3:1 has probability about 42%).
The click
The 3:1 ratio is a probability, not a guarantee. In a cross Aa × Aa, each child independently has a ¾ chance of showing the dominant trait (AA or Aa) and a ¼ chance of showing the recessive one (aa). The 3:1 ratio describes what you expect on average over many offspring, just as a fair coin gives about half heads over many flips but not exactly 2 heads in every 4.
For exactly 3 dominant and 1 recessive among 4 children, use the binomial formula: P = C(4,3) × (¾)³ × (¼) = 4 × 27/64 × 1/4 = 108/256 ≈ 0.42. It is the single most likely outcome, but it happens only about 42% of the time.
The other outcomes: all 4 dominant = (¾)⁴ = 81/256 ≈ 32%; 2 dominant and 2 recessive = 6 × (¾)² × (¼)² = 54/256 ≈ 21%; 1 dominant and 3 recessive = 12/256 ≈ 5%; all 4 recessive = 1/256 ≈ 0.4%. Together they add up to 256/256.
Mendel saw clean ratios because he counted large numbers of offspring. For seed shape in garden peas, his F₂ generation had 5474 round and 1850 wrinkled seeds, a ratio of about 2.96 : 1. Small samples scatter; large samples get close to the expected ratio.
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