An individual heterozygous for two alleles (AaBb) produces two million sperms. How many of the sperms will have both recessive alleles

Options

A. 0.5 million
B. 1 million
C. 2 million
D. 0.25 million

Explanation

To solve the problem of how many sperms will have both recessive alleles (aabb) produced by an individual heterozygous for two alleles (AaBb), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Genotype**: The individual is heterozygous for two traits, represented as AaBb. This means they have one dominant allele (A) and one recessive allele (a) for the first trait, and one dominant allele (B) and one recessive allele (b) for the second trait.

2. **Determine Possible Gametes**: When this individual produces gametes (sperms), the alleles segregate independently. The possible combinations of alleles in the gametes can be determined using the following combinations:
- From the A/a alleles, the possible gametes are A or a.
- From the B/b alleles, the possible gametes are B or b.

Therefore, the possible gametes produced will be:
- AB
- Ab
- aB
- ab

3. **Count the Total Gamete Types**: There are a total of 4 different types of gametes that can be produced from the AaBb genotype.

4. **Calculate the Proportion of Gametes with Recessive Alleles**: Out of the 4 gametes, only one gamete (ab) has both recessive alleles. Thus, the proportion of gametes with both recessive alleles is:
\[ \text{Proportion of ab} = \frac{1}{4} \]

5. **Calculate the Number of Sperms with Recessive Alleles**: Given that the individual produces 2 million sperms, we can calculate the number of sperms that will have both recessive alleles (ab) by multiplying the total number of sperms by the proportion of the ab gametes:
\[ \text{Number of ab sperms} = 2,000,000 \times \frac{1}{4} = 500,000 \]

6. **Final Answer**: Therefore, the number of sperms that will have both recessive alleles (aabb) is 500,000.

### Conclusion:
The final answer is that 500,000 of the sperms will have both recessive alleles.

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