Introduction to Math Topics in Biology

 Probability and Genetics

Introduction:

 

The purpose of this exercise is to allow explore the rules of probability.

 

Objectives:

o               Define the terms:  allele, dominant, recessive, and incomplete dominance.

o               Identify frequencies of allele combinations for single gene crosses.

o               Understand how to calculate the probability of different types of genetic events.

 

Materials:

            each group of students will need:

                        2 or more coins of different denominations

                        2 or more dice

 

Probability Activity:

 

Using two six-sided dice, perform the following exercises to explore the laws of probability.  Show all of your calculations!

      a.   Roll a single six-sided die.  What is the probability of rolling a four?

 

  1. Roll a single muli-sided die (choose one).   How many sides are on this die?

      What is the probability of rolling a four?

 

  1. What is the probability of a single rolled die coming up with a single dot, three times in a row?

 

d.   Roll one die 12 times:  record your results:  one(s______, two(s) ______,

      three(s) ______, four(s) ______, five(s) ______, six(es) ______.

      What is the probability of rolling a one (single dot) on the thirteenth roll?

 

e.   Roll two dice together (simultaneously). 

                  What is the probability rolling seven?

 

                  What is the probability rolling two (one dot on each die)?

 

                  What is the probability of rolling a one and a two together?

 

f.    If you rolled a six-sided die and a ten-sided die,

                  what is the probability of rolling a one and a two together?

 

Introduction:

 

The purpose of this exercise is to allow students to observe how single genetic traits get combined.  Student groups will use beads (or beans) to represent gene alleles and a random selection method.

 

Objectives:

o               Define the terms allele, dominant, recessive, and incomplete dominance.

o               Identify frequencies of allele combinations for single gene crosses.

o               Understand the proportions involved with genetics and simple gene crosses.

 

Materials:

            each group of students will need:

                        4 large beakers

                        100-200 colored (red) beads

                        100-200 clear beads

 

genetics Activity:

 

Students will observe how single genetic traits are combined, using non-biological alleles (beads of different colors). 

A red bead represents the red allele, R. 

A clear bead represents the white allele, r. 

In this case RR=red, Rr=red, rr=white.

b.            Put all (100-200) red beads in one beaker (beaker 1), this represents the homozygous red parent.  Put all (100-200) clear beads in one beaker (beaker 2), this represents the homozygous white parent.  This represents the P (parent) generation.

c.            Select one bead from each beaker.  This pair should be tallied (recorded).  Put this pair in beaker 3.  Select another pair of beads (one from beaker 1 and one from beaker 2).  Put this pair in beaker 4. 

d.            Continue step 2 until you have 50 pairs each in beakers 3 & 4.  (100 total pairs.)  Record the number of RR, rr and Rr pairs you selected in step three.  This represents the F1 generation.

e.            Select one bead from each beaker.  Continue to select pairs until all the beads have been selected.  Record the number of RR, rr, and Rr.

f.              Now assume the beads represent alleles for flower color. 

a.      Assume that R is dominant and r is recessive.  What color are the flowers in the F1 generation (and how many of each color)? What color are the flowers in the F2 generation (and how many of each color)?

b.      Assume that R and r show incomplete dominance.  What color are the flowers in the F1 generation (and how many of each color)? What color are the flowers in the F2 generation (and how many of each color)?