Genetic ratios are probability ratios. If for example, we mate (B=black dominant, b=gray recessive) two heterozygous black cows (Bb) and 4 offspring are produced , the ratio of 3 black and 1 gray should be possible . However, what are the chances of all black and all gray litters ?
To produce all gray cows our chances are

Options

A. `9//16`
B. `3//4`
C. `1//256`
D. `81//256`

Explanation

To solve the problem of determining the chances of producing all gray cows from a cross between two heterozygous black cows (Bb), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Genotypes of the Parents:**
- We have two heterozygous black cows, both with the genotype Bb (where B = black, b = gray).

2. **Determine the Gametes:**
- Each parent can produce two types of gametes: B (black) and b (gray). Therefore, the possible combinations of gametes from the two parents are:
- BB (homozygous black)
- Bb (heterozygous black)
- bB (heterozygous black)
- bb (homozygous gray)

3. **Construct the Punnett Square:**
- The Punnett square for this cross would look like this:

```
B b
------------
B | BB Bb
b | bB bb
```

- From the Punnett square, we can see the possible genotypes of the offspring:
- 1 BB (black)
- 2 Bb (black)
- 1 bb (gray)

4. **Calculate the Phenotypic Ratio:**
- The phenotypic ratio from this cross is:
- 3 black (BB and Bb) : 1 gray (bb)

5. **Determine the Probability of All Offspring Being Gray:**
- To find the probability of getting all gray offspring (bb), we need to calculate the probability of getting a gray offspring in one trial, which is:
- Probability of bb = 1/4 (since there is 1 bb out of 4 total genotypes).

6. **Calculate the Probability for Four Offspring:**
- For four offspring to all be gray, we calculate:
- Probability = (1/4) × (1/4) × (1/4) × (1/4) = (1/4)^4 = 1/256.

### Final Answer:
The probability of producing all gray cows (bb) from the cross of two heterozygous black cows (Bb) is **1/256**.

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