Download Laws of Probability: Coin Toss Lab

Name: Date: Period: Laws of Probability: Coin Toss Lab Few concepts have had greater effect on the science of genetics than the laws of probability.
Probability refers to the chance of something happening. Under normal conditions, probability
calculations can give us good ideas of what to expect from different genetic combinations. A
thorough understanding of probability was instrumental in leading Gregor Mendel to his basic
conclusions about genetics, and these same laws of probability play an essential role in genetics
today.
In this lab you will make predictions using Punnett Squares, you will then use pennies to simulate
the crosses. Then compare the Actual Ratios with the Predicted Ratios. The trait you are studying
in this lab is the result of a gene that codes for a short big toe in humans. T represents the
dominant allele, short big toe, and t is the recessive allele, long big toe. The following
genotypes are possible. Fill in the phenotypes for them.
Genotype
Phenotype (description)
T T
T t
t t
Part I: Probability and Mendel’s Law of Segregation
Individuals receive two alleles for each trait they inherit. These alleles are inherited from each of
their parents and are located on homologous chromosomes. During meiosis, homologous
chromosomes and the alleles they contain are segregated into separate gametes, resulting in haploid
gametes with one allele for each gene in the gametes.
1. If an individual inherits a heterozygous genotype (Tt), what is the chance that the gametes
they produce will contain the dominant allele (T)?
_______ out of _______ or ________%
2. If an individual inherits a heterozygous genotype (Tt), what is the chance that the gametes
they produce will contain the recessive allele (t)?
_______ out of _______ or ________%
Now we will simulate the process of meiosis and its effects by using a coin to represent an
individuals genotype. Heads on the coin will represent the dominant allele (T) and tails will
represent the recessive allele (t). Flipping the penny will simulate the segregation of alleles into
gametes. For a heterozygous individual, the probability of producing gametes with the dominant
allele (T) is equal to the probability of flipping heads on a penny and the probability of producing
gametes with the recessive allele (t) is equal to the probability of flipping tails on a penny. Flip the
penny and tally the results in the table below. Count the tallies and record this number in the last
two columns of the table.
Tally
T allele (heads)
Total
t allele (tails)
T
allele
(heads)
50 tosses
3. Does the result of the penny flipping simulation match the predictions you made fairly
closely? Why or why not?
t allele
(tails)
Part II: Probability and Fertilization
Flipping a single coin and the sorting of individual alleles for one trait into gametes during meiosis
are both examples of independent events. Predicting the outcome of these events is pretty
straightforward. But, how does probability operate with two independent events occurring
simultaneously, such as two coins being flipped at once? Or, in a genetics related example, what are
the chances of the same allele (T or t) ending up in the egg and sperm produced by two
heterozygous parents? Geneticists use Punnett squares to predict the chances of this happening
based on the parents genotypes.
Complete the Punnett Square to predict the possible genotypes of a zygote resulting from
fertilization between two gametes from heterozygous parents. (Tt x Tt)
T
t
Chance of TT zygote: _______ in 4 or _______ %
T
Chance of Tt zygote: _______ in 4 or _______ %
Chance of tt zygote: _______ in 4 or _______ %
t
Now you will determine the ratios by using pennies to represent the crosses. You will need two
pennies. The “heads” side of the penny represents the dominant allele (T) and “tails” represents the
recessive allele (t). This entire penny represents a parent that has the genotype Tt. A second penny
represents the other parent. One partner is going to play the role of female parent, the other will
play the role of male parent. When the coin is flipped, you are determining what allele the sperm or
egg is receiving during meiosis. When you put the alleles from the two flipped coins together, you
are simulating fertilization.
To determine actual probabilities, flip your coins 100 times, recording in the table below how often
each combination came up. (Use tally marks to record your data then summarize as a number)
Gene Combination
Homozygous Dominant
(2 heads)
Heterozygous
(1 head, 1 tail)
Homozygous Recessive
(2 tails)
Tally Marks
Total
Comparing Actual and Predicted Results
Predicted % Probability
(from Punnett square)
Homozygous Dominant
Heterozygous
Homozygous Recessive
Actual Result
(from flipping pennies)
Comparing the results from the punnett square and the coin flipping should reveal similar
results. This is because punnett squares apply two rules of probability to accurately make
predictions about the probability of certain genotypes resulting from parents of known
genotypes. The first rule is the rule of multiplication and the second is the rule of addition.
4. State the rule of multiplication.
5. State the rule of addition.
6. What is the probability of parent #1 producing gametes with dominant alleles (T) if parent
#1 is heterozygous (Tt)?
7. What is the probability of parent #2 producing gametes with dominant alleles (T) if parent
#1 is heterozygous (Tt)?
8. Producing a homozygous dominant (TT) zygote requires parent #1 to produce gametes with
a dominant allele (T) and parent #2 to produce a gamete with a dominant allele (T). Based
on the rule of multiplication what is the probability of two heterozygous parents producing a
homozygous dominant offspring? Please show how you calculated this.
9. According to the rule of multiplication what is the probability of two heterozygous (Tt)
parents producing a homozygous recessive (tt) zygote? Please show how you calculated this.
In order to produce homozygous dominant offspring (TT) or homozygous recessive (tt) offspring both
parents must produce gametes with the same allele, thus there is only one possible way their alleles
can be combined that will result in homozygous offspring. By contrast there are two different ways
that two heterozygous parents can produce heterozygous offspring. In possibility one, parent #1 can
pass on the dominant allele and parent #2 can pass on the recessive allele. In possibility two,
parent #1 passes on the recessive allele and parent #2 passes on the dominant allele. This is
accounted for in punnett squares by the fact that both possibilities are listed. In terms of the rules
of probability, this situation requires that we apply both the rule of multiplication AND the rule of
addition.
10. Two parents, who have the genotype Tt, can produce heterozygous offspring two ways. For
each possibility listed below, calculate the probability of the event. Please show how you
calculated this. (requires only the rule of multiplication)
Possibility 1: Parent #1 passes on the T allele and parent #2 passes on the t allele
and thus the offspring genotype is Tt.
Possibility 2: Parent 1 passes on the t allele and parent 2 passes on the T allele and
thus the offspring genotype is tT.
11. Using the rule of addition, what is the probability of two parents who are heterozygous for a
certain trait having offspring with a heterozygous genotype for that trait? Show how you
calculated this.
Additional Practice
12. Why was it necessary to flip the penny so many times to obtain a reliable result for these
simulations?
13. Do the Punnett squares in genetics problems tell you what must happen or what might
happen? Explain?
14. If three coins are flipped simultaneously, what is the probability that all three will be
heads? Show how you calculated this.
15. What is the probability that two of the coins are heads and one is tails? Show how you
calculated this.
16. A dog breeder is interested in producing a dog that is recessive for three separate genes
(aabbcc). The parent dogs are both heterozygous for all three genes (AaBbCc). What is the
probability that a puppy will have the desired genotype (aabbcc). Show how you calculated
this. Hint: requires the using the rule of multiplication more than once.
17. What is the chance of a parent who is heterozygous for a short big toe and a parent who is
homozygous dominant for a short big toe having one child that is heterozygous AND a
second child that is also heterozygous? Show how you calculated this.
18. According to the rules of probability, what is the chance that two parents who are
heterozygous for short big toes have a child who is heterozygous for short big toes OR a
child who is homozygous dominant for short big toes? Show how you calculated this using
the rule of probability, not a Punnett square. You may use a Punnett square to check your
answer.