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Probability and
Punnett Squares
Chapter 11-2
What are
the
chances?
What are the chances of snow?
And getting out of school?
Probability
 The
likelihood that a particular
event will occur.
Probability

What number will you get when rolling
a dice?
Probability
 When
flipping a coin, what are the
chances of getting
heads verses tails?
Genetics and Probability
Example
Event- flipping a quarter
Event outcome- quarter lands on heads
- quarter lands on tails

Question
Event
Event
outcome
Heads or tails?
The flip
Heads
Probability example (contd.)
Question
Heads or tails?
Event
The flip
Event outcome
Heads
Probabilities
Event outcome
Probability of the
event outcome
How?
Heads on single flip
1 out of 2 = 1/2
Of the 2 outcomes only, 1
heads, is turned over (1/2)
Both heads on 2 flips
1 out of 4 = 1/4
Each event is independent
of the other (1/2 X 1/2 =1/4)
1 out of 8 = 1/8
3 independent events
(1/2 X 1/2 X 1/2 = 1/8)
All heads on
1st 3 flips
Genetics and probability

How is probability associated with
genetics?

Much like the flipping of a quarter,
the segregation of alleles is
completely random.

Mendel realized this. He was then
able to explain the results of his
genetic crosses by probability and
math.
The Punnett Square
The principles of probability can be
used to predict the outcomes of genetic
crosses
 Punnett square – a way to show which
genes can combine when egg and
sperm join
 Alleles are represented by letters
 Capitol letters = Dominant genes T
 Lower case = Recessive genes
t

The Punnett Square

Genotype – all possible combinations
of genes


Represented by letters
T or t
Phenotype – physical appearance
of organism

Description of characteristic
 Tall or short
The Punnett Square
Parent’s gamete possibilities go out
side of the square
Sperm =>
 Male across
the top
 Female down
the side
<= Egg

The Punnett Square
If we cross two heterozygous tall
 Tt x Tt
T
t
Sperm =>
 Sperm
T
possibilities
 Egg
possibilities
<= Egg

t
The Punnett Square
Offspring (diploid zygote) possibilities
go
T
t
inside the boxes

Bring 1 letter down T
Bring 1 letter over
Capital letter first
Lower case letter t
second
=>




=>
T T
Tt
T t
tt
Probability


Can be determine by completing a Punnett
Square . What are the chances of having a boy?
Example:
X
Y
Probability of first offspring
being a male: 1/2
X
XX
XY
X
XX
XY
Probability


Probability does not change after traits show
up in an offspring.
Same chance still exists for every possibility
of being expressed.
X
Y
Probability of first offspring
being a male: 1/2
X
XX
XY
Probability of second
1/2
offspring being a male:
Probability of third
1/2
offspring being a male:
X
XX
XY
Probability Ratios




Probabilities predict the average outcome of
a large number of events
Probability can be expressed as a ratio,
fraction, or percent
A ratio is a proportion
 It compares quantities relative to each
other
The larger the sampling of individuals, the
closer the ratio will be to the predicted ratio
Genetic Ratios



Comparing the number of genotypes or
phenotypes of the possible offspring
Genotypic Ratio
 Comparing the amount of offspring that
express each allele combination in a given
cross
Phenotypic Ratio
 Comparing the amount of offspring that
express each physical trait in a given
cross
Example
brown

green
Genotypic Ratio
 There
is one homozygous
dominant, two
heterozygous, and one
homozygous recessive.
 The ratio is 1:2:1
 1BB:2Bb:1bb

Phenotypic Ratio
 There
are three browns
and one green.
 The ratio is 3:1
 3brown:1green
The Punnett Square
Lets do a punnett square
Trait- skin of pea seeds (smooth or wrinkled)
Alleles- S= smooth and s= wrinkled

Ss X Ss
SS
Smooth
Ss
Smooth
Ss
Smooth
ss
Wrinkled
Punnett Square Example
Mendel’sPure
Traits
in Pea Plants
Smooth X Pure Dented
2 Heterozygous Smooth Crossed
Mendel’s Work

Observed several traits
 Height:

Mated Pure Tall (TT) plants with short (tt)
plants
 Called

Tall (T) and Short (t)
Parent “P” generation
Offspring were always tall
offspring “F1”
generation
 F = Filius = SON!
T
T
 Called
t
t
Tt
Tt
Tt
Tt
Mendel’s Work
Are offspring pure or __________
heterozygous?
Mendel’s Work



Took F1 offspring and mated with each other
to produce F2 generation
About ¾ were tall; ¼ were short
Mendel concluded his plants were
heterozygous after seeing the results
T
T
t
TT
Tt
t
Tt
tt
Genetic Problems
Working with
Punnett Squares
The Punnett Square






Recall that for each trait, there are two genes (one
from the mother, one from the father)
Let’s use earlobes as an example
Free earlobes are dominant to
attached earlobes
FF = pure dominant; free earlobes
Ff = heterozygous; free earlobes
ff = pure recessive; attached earlobes
The Punnett Square

Complete the Punnett square to show the
cross between two heterozygous parents
Father’s Genes
F
f
Ff x Ff
Mother’s
Genes
F
f
FF
Ff
Ff
ff
The Punnett Square



What are the genotypes of offspring with free
earlobes? FF and Ff
If the genotype is ff, what will the phenotype
be?
Attached earlobes
Genotype Ratio: 1FF : 2Ff : 1ff
F
f
F
f
FF
Ff
Ff
ff
The Punnett Square
How many offspring will have free
earlobes? 3
 How many will have attached earlobes? 1

Mother’s Genes
F
f
Father’s
Genes
F
f
FF
Ff
Ff
ff
The Punnett Square




The type of chin a person has is also a genetic
trait
A person with a cleft chin has a small
indentation in the middle of their chin
Cleft chin = dominant trait
Smooth chin = recessive trait
The Punnett Square





I = cleft chin
i = smooth chin
What are all possible genotypes if the father is Ii and
mother is ii?
Ii, ii
What phenotypes will
I
i
the offspring have and
how many will there
Ii
be?
i
ii
2/4  cleft chin
2/4  smooth chin
i
Ii
ii