   Chapter 14.2, Problem 53E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONSGenetics 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 T (tall) and t (short). The gene T is dominant, so a plant with genotype (genetic makeup) TT or Tt is tall, whereas one with genotype 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 Tt , then the following chart gives the possible genotypes of the offspring: Parent 2 T t Parent 1 T TT Tt t Tt tt Find the probability that a given offspring of these parents will be (a) tall (b) short

To determine

(a)

To find:

The probability that a given offspring of these parents will be tall.

Explanation

Given:

There are two types of genes controlling the height of the plant denoted by T(tall) and t(short).

The possible genotypes of the offspring are as follows.

 Parent 2 T t Parent 1 t tT tt t tT tt

Approach:

P(E)=n(E)n(S)(1)

Here, P(E) is the probability of the event E.

n(E) is the number of elements in event E.

n(S) is the number of elements in the sample space S

To determine

(b)

To find:

The probability that a given offspring of these parents will be short.

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