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Answer :
- Cross Ww x ww yields $\frac{1}{2}$ heterozygous offspring.
- Cross Ww x WW yields $0$ homozygous recessive offspring.
- The probability of heterozygous offspring in the first cross is $\frac{1}{2}$.
- The probability of homozygous recessive offspring in the second cross is $0$.
$\boxed{0}$
### Explanation
1. Problem Analysis
We are given two separate genetic crosses and asked to determine the probabilities of specific offspring genotypes. First, we analyze the cross between a heterozygous male (Ww) and a homozygous recessive female (ww). Then, we analyze the cross between a heterozygous male (Ww) and a homozygous dominant male (WW).
2. Ww x ww Cross
For the first cross (Ww x ww), we construct a Punnett square to visualize the possible offspring genotypes:
| | W | w |
| :---- | :-- | :-- |
| w | Ww | ww |
| w | Ww | ww |
From the Punnett square, we can see that there are two possible genotypes for the offspring: Ww (heterozygous) and ww (homozygous recessive). Two out of the four possible outcomes are heterozygous (Ww). Therefore, the probability of heterozygous offspring is $\frac{2}{4} = \frac{1}{2}$.
3. Ww x WW Cross
For the second cross (Ww x WW), we construct a Punnett square to visualize the possible offspring genotypes:
| | W | w |
| :---- | :-- | :-- |
| W | WW | Ww |
| W | WW | Ww |
From the Punnett square, we can see that there are two possible genotypes for the offspring: WW (homozygous dominant) and Ww (heterozygous). None of the offspring have the ww (homozygous recessive) genotype. Therefore, the probability of homozygous recessive offspring is $\frac{0}{4} = 0$.
4. Final Answer
Therefore, for the first cross (Ww x ww), the probability of heterozygous offspring is $\frac{1}{2}$, and for the second cross (Ww x WW), the probability of homozygous recessive offspring is $0$.
### Examples
Understanding the probability of offspring genotypes is crucial in agriculture for predicting traits in crops or livestock. For example, a farmer might want to know the likelihood of certain disease-resistant genes being passed on to the next generation of plants.
- Cross Ww x WW yields $0$ homozygous recessive offspring.
- The probability of heterozygous offspring in the first cross is $\frac{1}{2}$.
- The probability of homozygous recessive offspring in the second cross is $0$.
$\boxed{0}$
### Explanation
1. Problem Analysis
We are given two separate genetic crosses and asked to determine the probabilities of specific offspring genotypes. First, we analyze the cross between a heterozygous male (Ww) and a homozygous recessive female (ww). Then, we analyze the cross between a heterozygous male (Ww) and a homozygous dominant male (WW).
2. Ww x ww Cross
For the first cross (Ww x ww), we construct a Punnett square to visualize the possible offspring genotypes:
| | W | w |
| :---- | :-- | :-- |
| w | Ww | ww |
| w | Ww | ww |
From the Punnett square, we can see that there are two possible genotypes for the offspring: Ww (heterozygous) and ww (homozygous recessive). Two out of the four possible outcomes are heterozygous (Ww). Therefore, the probability of heterozygous offspring is $\frac{2}{4} = \frac{1}{2}$.
3. Ww x WW Cross
For the second cross (Ww x WW), we construct a Punnett square to visualize the possible offspring genotypes:
| | W | w |
| :---- | :-- | :-- |
| W | WW | Ww |
| W | WW | Ww |
From the Punnett square, we can see that there are two possible genotypes for the offspring: WW (homozygous dominant) and Ww (heterozygous). None of the offspring have the ww (homozygous recessive) genotype. Therefore, the probability of homozygous recessive offspring is $\frac{0}{4} = 0$.
4. Final Answer
Therefore, for the first cross (Ww x ww), the probability of heterozygous offspring is $\frac{1}{2}$, and for the second cross (Ww x WW), the probability of homozygous recessive offspring is $0$.
### Examples
Understanding the probability of offspring genotypes is crucial in agriculture for predicting traits in crops or livestock. For example, a farmer might want to know the likelihood of certain disease-resistant genes being passed on to the next generation of plants.
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