A ratio such as 3:1 gives the chance for each offspring. It is not a count that every family must show, so a small family can look very different from the ratio.
This lesson follows reading a fictional pedigree. Once you can name genotypes, the next step is to say what they predict.
What is the difference between chance and count?
- Chance for one offspring: the probability that a single offspring shows the trait.
- Expected count: the average number you would see across many offspring.
Each offspring is independent, so earlier offspring do not change the chance for the next.
Worked example with an invented plant
An invented plant cross is Tt × Tt, where short (tt) is the recessive phenotype. The chance that one offspring is short is 1 in 4, or 0.25.
Question: If four offspring are produced, how likely is it that none are short, and that exactly one is short?
- The chance that one offspring is not short is 3 in 4, or 0.75.
- None short: all four must be tall, so (0.75)⁴ = 81 ÷ 256, which is about 31.6%.
- Exactly one short: the short one can be in any of 4 places. Each case has (0.25)(0.75)³ = 27 ÷ 256, so the total is 4 × 27 ÷ 256 = 108 ÷ 256, which is about 42.2%.
Written answer: “The chance that a single offspring is short is 1 in 4. In a family of four, about 32% of families would have no short offspring, and about 42% would have exactly one. The expected count of one short in four is an average, not a promise.”
Exactly one short is the most likely result, yet it still happens in fewer than half of families.
The mistake that loses marks
The common slip is to say, “The ratio is 3:1, so four offspring must give exactly three tall and one short.” But a ratio is only an expectation.
| Statement | Correct? |
|---|---|
| “Each offspring has a 1 in 4 chance of being short” | Yes |
| “Exactly one of four offspring will be short” | No |
| “After three tall offspring, the next is more likely to be short” | No, the chance stays 1 in 4 |
The fix is to write “chance for each offspring” or “expected” whenever you state a ratio.
A routine for chance questions
- State the chance for one offspring.
- Say whether the question asks about one offspring or several.
- For several, multiply independent chances.
- Use words such as “expected” or “chance”, not “will”.
The simple inheritance cross explorer lets you simulate many offspring and see how small samples vary.
Check yourself
Same cross. What is the chance that both of two offspring are short?
Answer
Each has a 1 in 4 chance and they are independent, so the chance is 1/4 × 1/4 = 1/16, or 6.25%.
What to study next
Move on to two genotypes that show the same phenotype. To revisit how the ratio arises, see completing monohybrid crosses.
If you want a teacher to go through the calculation with you, see online one-to-one Biology tuition.