Chapter 8.4, Problem 21PPS

a.

To determine

To find: How the combinations can be modeled by the square of a sum.

Explanation of Solution

If a person has the genetic combination $Tt$ . Then, half of his genes are dominant trait $T$ and the other half are the recessive trait $t$ .

So, his genes can be represented by $0.5T+0.5t$ .

If both parents have the genetic combination $Tt$ , then the outcomes for their children can be modelled by the sum of the square

  $\begin{array}{l}\left(0.5T+0.5t\right)\left(0.5T+0.5t\right)={\left(0.5T\right)}^2+2\left(0.5T\right)\left(0.5t\right)+{\left(0.5t\right)}^2\\ \left(0.5T+0.5t\right)\left(0.5T+0.5t\right)=0.25T^2+0.5Tt+0.5t^2\end{array}$

Therefore,

Combinations can be modeled by the square of a sum in this way.

b.

To determine

To find: Predict the percent of children that will have both dominant genes, one dominant gene, and both recessive genes.

Explanation of Solution

There are four total outcomes. For children to have two dominant genes, they would have $TT$ , which is a $25\%$ probability.

For children to have one dominany gene, they would have $Tt$ , which is a $50\%$ probability.

For children to have two recessive genes, they would have $tt$ , which is a $25\%$ probability.