Question

There are many married couples in which the husband and wife both carry a gene for cystic fibrosis but don't have the disease themselves. suppose we select one of these couples at random. according to the laws of genetics, the probability that their first child will develop cystic fibrosis is 0.25. interpret this probability as a long-run relative frequency

• if researchers randomly select 4 such couples, there will be exactly 3 couples that will have a first child who does not develop cystic fibrosis.
• if researchers randomly select 8 such couples, there will be exactly 2 couples that will have a first child who develops cystic fibrosis.
• if researchers randomly select 4 such couples, there will be exactly one couple that will have a first child who develops cystic fibrosis.
• if you take a random sample of 100 couples in which the husband and wife both carry a gene for cystic fibrosis, but do not have the disease themselves, 25 of such couples will find that their first child develops cystic fibrosis.
• if you take a very large random sample of couples in which the husband and wife both carry a gene for cystic fibrosis, but do not have the disease themselves, about 25% of such couples will find that their first child develops cystic fibrosis

Answer 1

In a couple where both parents are carriers of the cystic fibrosis gene, the probability their child will inherit CF is 0.25. This reflects an expected relative frequency in large populations, where about 25% of the offspring of carrier parents would have CF, as per Mendel's observations and Punnett square predictions. (option 5 is the correct answer).

Step-by-step explanation:

Interpreting the Probability of Inheriting Cystic Fibrosis

The probability that a child will develop cystic fibrosis (CF) when both parents are carriers of the gene is 0.25, or 25%. This is because CF is an autosomal recessive disorder, meaning a child needs to inherit two copies of the mutated gene, one from each parent, to express the disease. When looking at the relative frequency of CF in a large population, if each couple has many children, approximately one in four would be expected to have CF, though actual outcomes may vary due to chance.

The inheritance pattern for CF is represented by a 3:1 ratio of unaffected to affected children, which Mendel also observed in his studies with pea plants. However, due to variability and chance, a couple might have more or fewer children with CF than the statistic predicts. Nevertheless, in a large sample of couples, the long-run frequency would approximate 25% of children being affected by CF, as illustrated by calculations based on Punnett squares and research data on carrier frequency and disease prevalence.

For example, researchers might find that in a group of 100 couples who are both carriers of the CF gene, about 25 children would be predicted to develop CF, conforming to the predicted pattern. Similarly, in a sample of eight such couples, we would expect on average two children to develop CF, though the exact number could deviate from this expectation due to random chance.