Genetic Allele Probability
1. **Stating the problem:**
We have two parents with alleles at a genetic locus. Parent 1 has alleles A and a, Parent 2 has alleles a and a. We want to find probabilities for offspring genotypes.
2. **Understanding allele inheritance:**
Each offspring receives one allele from each parent. Parent 1 can pass either A or a with equal probability $\frac{1}{2}$ each.
Parent 2 can only pass allele a (probability 1).
3. **Calculating probabilities:**
**a. Probability offspring receives A or a:**
Since offspring must receive one allele from each parent, possible alleles are A or a from Parent 1 and a from Parent 2.
Thus, offspring alleles are either A and a or a and a.
Probability of receiving A (from Parent 1) is $\frac{1}{2}$.
Probability of receiving a (from Parent 1) is $\frac{1}{2}$.
Parent 2 always passes a.
So, probability offspring receives A or a allele is 1 (certain) because offspring always gets either A or a from Parent 1 and a from Parent 2.
**b. Probability offspring receives two a alleles:**
This happens if Parent 1 passes a (probability $\frac{1}{2}$) and Parent 2 passes a (probability 1).
So, probability = $\frac{1}{2} \times 1 = \frac{1}{2}$.
**c. Probability offspring receives two A alleles:**
Parent 2 has only a alleles, so offspring cannot receive two A alleles.
Probability = 0.
**Final answers:**
- a) Probability offspring receives A or a allele = 1
- b) Probability offspring receives two a alleles = $\frac{1}{2}$
- c) Probability offspring receives two A alleles = 0