To calculate the probability that both siblings are affected by the disease in a family with two children, we need to consider the mode of inheritance.
Since the disease is inherited via a dominant mode of inheritance, if one parent is affected, there is a 1 in 2 chance that they carry the dominant disease-causing gene.
For the first child, there are two possibilities: they can either inherit the disease-causing gene from the affected parent or not inherit it.
If the first child inherits the disease-causing gene, there is a 1 in 2 chance that the second child will also inherit it.
If the first child does not inherit the disease-causing gene, there is a 0 chance that the second child will inherit it.
So, to calculate the probability that both siblings are affected, we multiply the probabilities together:
(1/2) * (1/2) = 1/4
Therefore, the probability that both siblings are affected is 1 in 4.
To calculate the probability that exactly one sibling is affected by the disease in a family with two children, we can consider two scenarios:
1. The first child inherits the disease-causing gene and the second child does not.
- The probability of the first child inheriting the gene is 1/2.
- The probability of the second child not inheriting the gene is also 1/2.
- So, the probability of this scenario is (1/2) * (1/2) = 1/4.
2. The first child does not inherit the disease-causing gene and the second child does.
- The probability of the first child not inheriting the gene is 1/2.
- The probability of the second child inheriting the gene is also 1/2.
- So, the probability of this scenario is (1/2) * (1/2) = 1/4.
To find the probability that exactly one sibling is affected, we add the probabilities of the two scenarios:
1/4 + 1/4 = 2/4 = 1/2
Therefore, the probability that exactly one sibling is affected is 1 in 2.