Question

If we cross between homozygous black rough (BBRR) guinea pig and homozygous white smooth guinea pig (bbrr), it produces black and rough animals in the ${ F }_{ 1 }$ generation. Presuming the genes to be present on a different chromosome, the percentage of ${ F }_{ 2 }$ individuals which are heterozygous for both gene pairs would be
(a)25%
(b)35%
(c)50%
(d)75%

Answer 1

Hint: When we cross between a homozygous black rough (BBRR) guinea pig and homozygous white smooth guinea pig (bbrr), we expect a characteristic ${ 1 }{ : }{ 2 }{ : }{ 1 }{ : }{ 2 }{ : }{ 4 }{ : }{ 2 }{ : }{ 1 }{ : }{ 2{ : }{ 1 } }$ ratio of the nine possible genotypes. These nine genotypes can be grouped into four phenotypes.

Complete answer:
A cross between two different lines/genes that differ in two observed traits is called a dihybrid cross., There is a relationship of completely dominant - recessive traits between the alleles of both the loci according to Mendel's statement. For example, BBRR/bbrr parents result in ${ F }_{ 1 }$ offspring that are heterozygous for both B and R (BbRr). Here in this term "Dihybrid cross", the "di" indicates that there are two traits involved (e.g. B and R), the meaning of "hybrid" is that each trait has two different alleles (e.g. B and b, or R and r), and the term "cross" means that there are two individuals (usually a mother and father) are combining or "crossing" their genetic information.
So, if we do a cross between guinea pigs having homozygous black rough (BBRR) homozygous white smooth (bbrr), it will produce black rough guinea pigs(BbRr) in the ${ F }_{ 1 }$ generation, if one can find all the genes on the same chromosomes for the given traits, in the ${ F }_{ 2 }$ generation, $6.25%$ are homozygous black rough(BBRR), homozygous white, smooth(bbrr), homozygous black and white(BBrr), homozygous white, rough(bbRR), $12.5%$ are homozygous black heterozygous rough(BBRr), heterozygous black, homozygous rough(BbRR), heterozygous black homozygous white(Bbrr), homozygous white, heterozygous rough(bbRr), $25%$ are heterozygous Black and rough are formed.

	BR	bR	Br	br
BR	BBRR	BbRR	BBRr	BbRr
bR	BbRR	bbRR	BbRr	bbRr
Br	BBRr	BbRr	BBrr	Bbrr
br	BbRr	bbRr	Bbrr	bbrr

1) As applied to the dihybrid, the rules of meiosis are codified in Mendel's first law and Mendel's second law, which is also called the Law of Segregation and the Law of Independent Assortment, respectively.
2) four identical offspring is produced by the first filial generation as a result of the cross, the second filial generation, which occurs by crossing the members of the first filial generation, shows a ${ 9 }{ : }{ 3 }{ : }{ 3 }{ : }{ 1 }$ phenotypic ratio.
3) The Punnett square shown above is a square diagram that is used to predict the genotypes of a particular cross or breeding experiment which is named after Reginald C. Punnett, and biologists used this table to determine the probability of an offspring having a particular genotype.
So, the correct answer is, ‘25%’.
Note: When Mendel made this cross, he already knew the dominance relationship between alleles for each trait, and the purpose of his dihybrid cross was to determine if any relationship existed between different allelic pairs.