Final answer:
The chance of the next fawn having brown fur with white spots is 75%, as the parents are heterozygous (Bb) and three out of four combinations from a Punnett square result in the dominant phenotype.
Step-by-step explanation:
The question involves understanding the basic principles of genetics and the use of a Punnett square to predict the inheritance pattern of a dominant trait over a recessive one in white-tailed deer. The key to solving this problem is recognizing that since the offspring have dark brown fur, which is recessive (b), both parents must carry the allele for dark brown fur despite displaying the dominant phenotype of brown fur with white spots. Hence, they are heterozygous, carrying one dominant (B) and one recessive (b) allele each.
When setting up a Punnett square with both parents as Bb, the four possible offspring combinations are BB, Bb, Bb, and bb. The first three combinations (BB, Bb, Bb) result in the brown fur with white spots, and only the last combination (bb) results in the all dark brown fur phenotype. This gives us three out of four combinations, or 75% probability, for brown fur with white spots in the next fawn.