Is Pompe disease an autosomal recessive disorder?

The probability that their children will have the disease is dependent on knowing the genotype of the father. Since his brother died of the disease, we know that his brother was homozgyous recessive. Therefore, their parents must have both been carriers (note that we have to assume that neither of the parents had the disease because they would be unlikely to survive to reproductive age). Usually a cross between two carriers would give offspring in a 1:2:1 ratio of homozyous normal : heterozygous : homozygous recessive. However, since the man doesn't have the disease, we can eliminate the homozygous recessive in the probability equation and so this means that he is either homozygous normal (1/3 chance) or heterozygous carrier (2/3 chance). So the man has a 2/3 chance of being a carrier. If he is a carrier, then the probability that the man would pass on the recessive allele would be 1/2. So, the probability that he is a carrier AND that he would pass on the recessive allele is 2/3 x 1/2 = 2/6 = 1/3. Since his wife is a carrier, then she has a probability of passing on the recessive allele of 1/2. So, the probability that they would have an affected child is the product of both probabilities: 1/3 x 1/2 = 1/6.

Pompe disease has become a public concern nowadays.Without more info about the man you cannot answer the question. Since the man does not have the disease, we know that the man is either heterozygous or homozygous dominant. Just because his brother was homozygous recessive, that does not tell us anything about the man himself. All we know is that both of the man's parents had at least one recessive allele, but they could have had the disease too because it is not necessarily fatal before the person has children (some people can be asymptomatic for their whole lives)

If the man is homozygous dominant, then the children have a 0% chance of getting the disease because they will be 50% homozygous dominant and 50% heterozygous.

If the man is heterozygous, then there is a 25% chance of getting the disease (homozygous recessive), 50% of being heterozygous, and 25% chance of being homozygous dominant.