If both parents are heterozygous for a trait, the probability that an offspring will be recessive for that trait is?

Analyze the question: Both parents are heterozygous (Aa × Aa). We need the probability that an offspring is recessive (aa).

Concept: Each heterozygous parent produces two kinds of gametes, A and a, in equal proportions (½ each), according to Mendel's law of segregation. A Punnett square shows the possible combinations.

Solution:

Parents: Aa × Aa

Gametes: (A or a) × (A or a)

| | A | a | |---|---|---| | A | AA | Aa | | a | Aa | aa |

Offspring genotypes:

• 1 AA (homozygous dominant)
• 2 Aa (heterozygous)
• 1 aa (homozygous recessive)

Genotypic ratio = 1 : 2 : 1 Phenotypic ratio = 3 dominant : 1 recessive

A recessive offspring must be aa, so the probability is:

P(a from father) × P(a from mother) = ½ × ½ = ¼

Check the options:

• A (½): this is the probability of a heterozygous offspring, not a recessive one.
• B (¾): this is the probability of showing the dominant trait.
• C (¼): correct.
• D (1): would only happen if both parents were aa.

Exam tip: For any Aa × Aa cross, remember the numbers ¼, ½, ¼ (AA, Aa, aa) and ¾ : ¼ for dominant : recessive appearance. If a question asks about the "recessive" offspring, think "aa = ¼".