Chapter 7.3, Problem 38E

To determine

To describe: Two ways to determine the percent of possible gene combinations that result in green pods

Answer to Problem 38E

First way is to look at the coefficients of the polynomial, second way is to figure the percentage by counting each kind of offspring in the punnett square.

Explanation of Solution

Given information: Any gene combination having even a single G gene will result in green pod.

Calculation:

First way

Given polynomial:-

  ${(0.5G+0.5y)}^2=0.25G^2+0.5Gy+0.25y^2$

Coefficient of $G^2$ is $0.25$

Coefficient of $Gy$ is $0.5$

As gene combination with even one $G$ results in green pod

  $\therefore$ Total percentage of green pods $=25\%+5\%$$=75\%$

Coefficient of $y^2$ is 0.25

  $\therefore$ Total percentage of yellow pods $=25\%$

Second Way

Punnett square implies that there total $4$ gene combination, namely GG, Gy, Gy, yy

As presence of even one G results in green pod, out of these $4$ combinations $3$ result in green pod and one (yy) results in yellow pod.

  $\therefore$ Probability of green pod $=\frac{3}{4}$$=0.75$

Percentage of green pod $=75\%$

Probability of yellow pod $=\frac{1}{4}$$=0.25$

Percentage of yellow pod $=25\%$