Final answer:
The proportion of F2 guinea pigs expected to be red and solid colored from a cross between two heterozygous F1 individuals, with BbSs genotypes, is calculated to be 3/16, or roughly 18.75%.
Step-by-step explanation:
In a cross of guinea pigs where brown coat color allele (B) is dominant over red (b), and the solid color allele (S) is dominant over spotted (s), we use a Punnett square to determine the genotypic and phenotypic outcomes for the F2 generation. The true-breeding parents would have genotypes BBSS and bbss, and their F1 offspring would all be heterozygous BbSs. To find the proportion of the F2 offspring that would be red and solid colored, we cross two F1 heterozygotes (BbSs x BbSs).
To calculate this, we know that the red coat color is recessive, so we need homozygous recessive bb, and for solid color, we can have either Bs or SS, but since red and solid colored is asked, we are looking for the BbSs x BbSs cross that results in bbS_. This results in a 1/4 chance of being bb for coat color and a 3/4 chance of being at least S_ for the solid pattern. Multiplying these probabilities together gives us the proportion of red and solid-colored offspring as 1/4 x 3/4 = 3/16, or roughly 18.75%.