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Suppose the brown allele for eye color (B) is completely dominant over the blue allele for eye color (b). If two brown-eyed parents produce a child that is blue-eyed, what is the probability that at least one out of the next two children they produce will also have blue eyes?
  • a)
    2.5%
  • b)
    25%
  • c)
    44%
  • d)
    50%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Suppose the brown allele for eye color (B) is completely dominant over...
If both parents have brown eyes (genotype BB), but they produce a child with blue eyes, it means that both parents must be heterozygous carriers for the blue eye allele (genotype Bb).
There is a 25% chance (1 out of 4) of having a child with the genotype bb, which corresponds to blue eyes.
Now, we need to calculate the probability of having at least one out of the next two children with blue eyes. We can calculate the probability of the complement event (both children having brown eyes) and subtract it from 1 to get the desired probability.
The probability of having both children with brown eyes is (3/4) x (3/4) = 9/16. Therefore, the probability of having at least one child with blue eyes is 1 - (9/16) = 7/16.
Converting 7/16 to a percentage, we get approximately 43.75%, which is closest to option C, 44%.
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Most Upvoted Answer
Suppose the brown allele for eye color (B) is completely dominant over...
Understanding the Genetics
- The brown allele (B) is dominant, and the blue allele (b) is recessive.
- Brown-eyed parents can have the following genotypes: BB (homozygous dominant) or Bb (heterozygous).
- Since they produced a blue-eyed child (bb), both parents must be carriers of the blue allele, making their genotype Bb.
Determining the Probability of Blue-Eyed Children
- The Punnett square for two Bb parents shows the possible genotypes of their offspring:
- BB: Brown eyes
- Bb: Brown eyes
- bB: Brown eyes
- bb: Blue eyes
- The breakdown of probabilities is as follows:
- BB: 25%
- Bb: 50%
- bb: 25%
- Therefore, the probability of having a blue-eyed child (bb) is 25%.
Calculating the Probability for Two Children
- We want the probability that at least one out of the next two children has blue eyes.
- The easiest way to calculate this is to find the probability that neither child has blue eyes, and then subtract that from 1.
Probability of No Blue-Eyed Children
- The probability that one child does not have blue eyes is 75% (100% - 25%).
- For two children, the probability that both do not have blue eyes is:
- 0.75 * 0.75 = 0.5625 or 56.25%.
Final Calculation
- To find the probability that at least one of the two children has blue eyes, subtract the above result from 1:
- 1 - 0.5625 = 0.4375 or 43.75%.
- Rounding gives approximately 44%, making option 'C' the correct answer.
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