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Genetics In deer, the gene N is for normal coloring and the gene a is for albino. Any gene combination with an N results in normal coloring. The Punnett square shows the possible gene combinations of an offspring and the resulting colors when both parents have the gene combination Na.
(a) What percent of the possible gene combinations result in albino coloring?
(b) Each parent’s gene combination is represented by the polynomial 0.5N + 0.5a. The product (0.5N + 0.5a)2 represents the possible gene combinations of an offspring. Find this product.
(c) The coefficient of each term of the polynomial you wrote in part (b) is the probability (in decimal form) of the offspring having that gene combination. Use this polynomial to confirm your answer in part (a). Explain.

Sagot :

The breeding of the genetics in a deer, in which the parents have both a

N and and a allele results a 0.25 chance of an albino coloring.

Response:

(a) 25%

(b) (0.5·N + 0.5·a)² = 0.25·N·N + 0.25·N·a + 0.25·N·a + 0.25·a·a

(c) The coefficient of the product (offspring) a·a is 0.25 which confirms the response in part (a)

What is Punnett square and how is it used?

A Punnett square is used for the prediction of the genotypes in a

breeding experiment.

The Punnett square for the possible gene combinations is presented as

follows;

[tex]\begin{tabular}{|c|c|c|c|}&& P2& \\&&N&a\\P1&N&NN normal &Na normal\\&a&Na normal&aa albino\end{array}\right][/tex]

(a) Number of possible gene combination resulting in albino coloring = 1

Number of possible gene combinations = 4

The percentage of the possible gene combination resulting in albino

coloring is therefore;

[tex]Percentage = \dfrac{1}{4} \times 100 = \underline{25\%}[/tex]

(b) The polynomial of each parent gene combination = 0.5·N + 0.5·a

The product that represent the possible gene combinations of an offspring = (0.5·N + 0.5·a)²

(0.5·N + 0.5·a)² = (0.5·N + 0.5·a) × (0.5·N + 0.5·a)

(0.5·N + 0.5·a)×(0.5·N + 0.5·a) = 0.25·N·N + 0.25·N·a + 0.25·N·a + 0.25·a·a

The product is therefore;

  • (0.5·N + 0.5·a)² = 0.25·N·N + 0.25·N·a + 0.25·N·a + 0.25·a·a

(c) From the product of the polynomial, (0.5·N + 0.5·a)², the probability

and therefore, the percentage of the possible gene combinations that

result in albino, a·a is 0.25, which is 25%.

  • The coefficient of a·a confirms the percentage of the possible gene combinations that result in albino in part (a) is 25%.

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