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Genetic ratios are probability ratios. I...

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 black cows our chances are

A

`9//16`

B

`1//4`

C

`3//4`

D

`81//256`

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To solve the problem of determining the chances of producing all black cows from a mating of two heterozygous black cows (Bb), we can follow these steps: ### Step 1: Understand the Genetic Makeup - We have two heterozygous black cows, both represented as Bb (where B is the dominant black allele and b is the recessive gray allele). ### Step 2: Determine Gametes - Each parent (Bb) can produce two types of gametes: B and b. Therefore, the possible gametes from both parents are: - Parent 1: B or b - Parent 2: B or b ### Step 3: Create a Punnett Square - We can create a Punnett square to visualize the potential offspring: ``` B b ---------------- B | BB Bb | b | Bb bb ``` ### Step 4: Analyze the Offspring Genotypes - From the Punnett square, we can see the possible genotypes of the offspring: - BB (homozygous black): 1 out of 4 (1/4) - Bb (heterozygous black): 2 out of 4 (2/4) - bb (homozygous gray): 1 out of 4 (1/4) ### Step 5: Calculate the Probability of All Black Offspring - To have all black offspring, we need all offspring to be either BB or Bb. The only genotype that is not black is bb. - The probability of getting 4 black offspring (all BB or Bb) can be calculated as follows: - The chance of getting a black offspring (BB or Bb) from one mating is 3 out of 4 (3/4). - The probability of getting 4 black offspring in a row is (3/4) multiplied by itself 4 times (since each offspring is an independent event): \[ \text{Probability of all black} = \left(\frac{3}{4}\right)^4 = \frac{81}{256} \] ### Step 6: Calculate the Probability of All Gray Offspring - To have all gray offspring, we need all offspring to be bb. - The probability of getting a gray offspring (bb) from one mating is 1 out of 4 (1/4). - The probability of getting 4 gray offspring in a row is (1/4) multiplied by itself 4 times: \[ \text{Probability of all gray} = \left(\frac{1}{4}\right)^4 = \frac{1}{256} \] ### Final Results - The chances of producing all black cows: **81/256** - The chances of producing all gray cows: **1/256**
To solve the problem of determining the chances of producing all black cows from a mating of two heterozygous black cows (Bb), we can follow these steps: ### Step 1: Understand the Genetic Makeup - We have two heterozygous black cows, both represented as Bb (where B is the dominant black allele and b is the recessive gray allele). ### Step 2: Determine Gametes - Each parent (Bb) can produce two types of gametes: B and b. Therefore, the possible gametes from both parents are: - Parent 1: B or b ...
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