To determine the probability of a child being a carrier in the F3 generation, we analyze the transmission of a recessive gene (e.g., autosomal recessive or sex-linked recessive like Haemophilia or Colour Blindness ).

Assuming a standard pedigree scenario where a carrier parent in the F1 generation passes the allele to the F2 generation, who then passes it to F3:

1. F1 to F2: If one parent in F1 is a carrier (heterozygous, ) and the other is normal homozygous (), the probability of the F2 offspring being a carrier () is 1/2.
2. F2 to F3: If this F2 carrier () marries a normal individual (), the probability of their child (F3) being a carrier () is also 1/2.
3. Total Probability: The combined probability is the product of the probabilities at each step: .

Thus, there is a 1/4 chance for the birth of a carrier child in the F3 generation.