Q) In cattle, polled (hornless) (H) is dominant to horned (h), while black coat (B)
is dominant to red (b). The two gene assort independently of each other and
i) If a pure breeding line of polled black cattle was crossed with a pure breeding breed that had horns and a red coat, what would u expect in the hybrids, and in the F2 produced by crossing between the F1 animals.
ii) How would the above answer change if there was a linkage between the H and B genes? (you could answer this by using a particular example value of the linkage between the genes, say 20%)
No problem. Standard dihybrid cross. Thank you for saying that they sort independently.
Part 1: First animal is HHBB and is crossed with hhbb. The resulting offspring will all be HhBb. That makes them all polled (hornless) and black.
If you take an HhBb and cross it with another HhBb you get a variety of results. I am assuming that your question only wants the possible phenotypes of the cross. There are four different phenotypes that could be produced. Polled/Black, Polled/Red, Horned/Black, and Horned/Red. The expected phenotypic ratio of that cross would be 9:3:3:1. 9 would be polled/black, 3 polled/red, 3 horned/black, and 1 horned/red. The genotypic ratio would be 1:2:1:2:4:2:1:2:1
Part 2: This cross will produce the same results as a monohybrid cross, since the genes are linked. The F1 generation will all be polled/black. That's no different than part one. The F2 is where the expected ratio goes back to a genotypic 1:2:1 and a phenotypic 3:1. 1 will be HHBB, 2 will be HhBb, and 1 will be hhbb. That makes 3 of them polled/black and 1 horned red.