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Question Video: Determining the Probability of Phenotypes from Dihybrid Crosses Biology

Assume that in guinea pigs, the allele for black fur (B) is dominant to the allele for white fur (b), and the allele for smooth fur (F) is dominant to the allele for rough fur (f). A guinea pig with genotype Bbff is crossed with a guinea pig with genotype bbFF. What is the probability, in percent, that the offspring will have black, smooth fur?

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Video Transcript

Assume that in guinea pigs, the allele for black fur, capital B, is dominant to the allele for white fur, lowercase b, and the allele for smooth fur, capital F, is dominant to the allele for rough fur, lowercase f. A guinea pig with the genotype capital B lowercase b lowercase f lowercase f is crossed with a guinea pig with the genotype lowercase b lowercase b capital F capital F. What is the probability, in percent, that the offspring will have black, smooth fur?

Let’s see. How can we determine the probability of offspring having certain traits? By using a Punnett square. In this question, we’re asked about two different traits, fur color and fur texture, which we’re told are controlled by two different genes, the B gene and the F gene. In order to use a Punnett square to solve this problem, we first need to determine all of the different combinations of alleles that we might find in the gametes of each parent. One parent has the genotype capital B lowercase b lowercase f lowercase f, and the other parent has the genotype lowercase b lowercase b capital F capital F.

Since we’re dealing with two different genes, in order to determine all of the different combinations of alleles that we might find in gametes of each parent, we should use the FOIL method. First, we can combine the first alleles of each gene to find our first possible combination of alleles in a gamete. Then, we can combine the two outer alleles and the two inner alleles and finally the two last alleles. In this way, we’ve determined all of the possible allele combinations for each parent’s gametes. And we can now place them on our Punnett square.

Since we see that we have listed four different possible combinations for each parent, we will need to create a four-by-four Punnett square. Then, we can place the gametes of one parent across the top of the Punnett square and the gametes of the other parent down the side of the Punnett square. Now our Punnett square is set up, and all we have to do is fill it in. We fill out our Punnett square by combining the alleles from the column header with the alleles from the row header. The convention is to keep the alleles for each gene next to each other and put any dominant allele for a gene before any recessive allele for that gene. This just makes the results easier to read. If we do the same in all of the remaining boxes in the Punnett square, we should end up with results that look like this.

The question asked us about offspring with black, smooth fur. In order to have black fur, the guinea pig just needs to have one capital B allele, since it is a dominant allele. Likewise, in order to have smooth fur, the guinea pig just needs to have one capital F allele, since it is also a dominant allele. So guinea pigs with black, smooth fur could have any of these genotypes. Let’s look for these genotypes in our Punnett square. Out of the total 16 squares on our Punnett square, eight of them have at least one dominant allele for each gene. So the probability that the offspring will have black, smooth fur is eight out of 16.

However, we’re asked for the probability in percent. So, to convert our fraction into percent, we can do this quick calculation or simply recognize that eight is half of 16. Either way, we should come to the conclusion that the probability in percent that the offspring will have black, smooth fur is 50 percent.

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