Textbook Problem

APPLICATIONS

Genetics Many genetic traits are controlled by two genes, one dominant and one recessive. In Gregor Mendel’s original experiments with peas the genes controlling the height of the plant are denoted by $\text{T}$ (tall) and $\text{t}$ (short). The gene $\text{T}$ is dominant, so a plant with genotype (genetic makeup) $\text{TT}$ or $\text{Tt}$ is tall, whereas one with genotype $\text{tt}$ is short. By a statistical analysis of the offspring in his experiments, Mendel concluded that offspring inherit one gene from each parent and that each possible combination of the two genes is equally likely. If each parent has the genotype $\text{Tt}$, then the following chart gives the possible genotypes of the offspring:

		Parent $2$
		$\text{T}$	$\text{t}$
Parent $1$	$\text{T}$	$\text{TT}$	$\text{Tt}$
	$\text{t}$	$\text{Tt}$	$\text{tt}$

Find the probability that a given offspring of these parents will be

(a) tall

(b) short