Identical twins are produced from the same sperm and egg (which splits after the first mitotic division), whereas fraternal twins are produced from separate sperm and separate egg cells. If two parents, one with brown eyes (a dominant trait) and the other with blue eyes (the recessive trait) produce one twin boy with blue eyes, what is the probability that a fraternal twin will transmit the blue eye allele to his or her offspring

This is 25%

Explanation:

Analysis, Since the dominant brown eyed parents produce blue eye child, this shows they are heterozygote dominant

However, this fraternal twin is not genetically identical, due to the blue eye color, (recessive) but the fact remain that they are the parents. (because he inherited the recessive allele from each of the parent) Therefore the probability is 25%.

This is because he is the only one out of the 4 kids (based on Mendelian fashion) this is 1/4,25%