Final answer:
The chance that all four offspring from a cross between a brown mouse and a heterozygous black mouse will be brown is 6.25%. Each offspring has a 50% chance of being brown (bb), and the calculation for all four is (1/2)^4.
Step-by-step explanation:
To determine the chances that all four offspring of a cross between a brown mouse and a heterozygous black mouse will be brown, we first need to understand the genetics involved. Black is a dominant trait and brown is a recessive trait. Therefore, the brown mouse can only have the genotype bb (homozygous recessive), while the heterozygous black mouse has the genotype Bb.
Using a Punnett square to represent the cross, we can predict the offspring's genotypes. Each offspring has a 1 in 2 chance of inheriting the recessive allele 'b' from the black parent, and a guaranteed 'b' from the brown parent. Therefore, each offspring has a 50% chance of being brown (bb). To find the probability of all four offspring being brown, we calculate (1/2)^4 (since each event is independent), which equals 1/16 or 6.25%.
The phenotypic ratio for a typical monohybrid cross of two heterozygotes (Bb) would be 3:1, where three-quarters of the offspring express the dominant phenotype and one-quarter express the recessive phenotype.