probability and punnett squares chapter 11-2 what are the chances?
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Probability and Punnett Squares
Chapter 11-2Chapter 11-2
What are the
chances?
What are the chances of snow?
And getting out of school?
Probability The The likelihoodlikelihood that a particular that a particular
event will occur.event will occur.
Probability
What number will you get when rolling What number will you get when rolling a dice?a dice?
Probability When flipping a coin, what are the When flipping a coin, what are the
chances of gettingchances of gettingheads verses tails?heads verses tails?
Genetics and Probability
Example
Event- flipping a quarter
Event outcome- quarter lands on heads
- quarter lands on tails
Heads or tails? The flip Heads
Question EventEvent
outcome
Probability example (contd.)Question Event Event outcome
Heads or tails? The flip Heads
Probabilities
Event outcome Probability of the event outcome
Heads on single flip 1 out of 2 = 1/2
Both heads on 2 flips 1 out of 4 = 1/4
All heads on 1st 3 flips
1 out of 8 = 1/8
How?Of the 2 outcomes only, 1 heads, is turned over (1/2)
Each event is independent of the other (1/2 X 1/2 =1/4)
3 independent events
(1/2 X 1/2 X 1/2 = 1/8)
Genetics and probability How is probability associated with How is probability associated with
genetics?genetics?
Much like the flipping of a quarter, Much like the flipping of a quarter, the the segregation of allelessegregation of alleles is is completely random.completely random.
Mendel realized this. He was then Mendel realized this. He was then able to able to explainexplain the results of his the results of his genetic crossesgenetic crosses by probability and by probability and math.math.
The Punnett Square The principles of probability can be used to The principles of probability can be used to
predictpredict the the outcomesoutcomes of genetic crosses of genetic crosses Punnett squarePunnett square – a way to show which – a way to show which
genes can genes can combinecombine when egg and sperm when egg and sperm joinjoin
Alleles are represented by Alleles are represented by lettersletters Capitol letters = Capitol letters = DominantDominant genes genes TT Lower case = Lower case = RecessiveRecessive genes genes tt
The Punnett Square GenotypeGenotype – all possible combinations
of genes Represented by letters T or tT or t
PhenotypePhenotype – physical appearance of organism Description of characteristiccharacteristic Tall or shortTall or short
The Punnett Square Parent’s gameteParent’s gamete possibilities go out possibilities go out
side of the squareside of the square Male across Male across
the topthe top Female down Female down
the sidethe side
Sperm =>
<=
Eg
g
The Punnett Square If we cross two If we cross two heterozygousheterozygous tall tall Tt x Tt x Sperm Sperm
possibilitiespossibilities Egg Egg
possibilitiespossibilities
Sperm =>
<=
Eg
g
TT tt
TT
tt
TtTt
The Punnett Square Offspring (Offspring (diploiddiploid zygote) possibilities zygote) possibilities
gogo inside the boxes inside the boxes
Bring 1 letter Bring 1 letter downdown Bring 1 letter Bring 1 letter overover Capital letter Capital letter firstfirst Lower case letterLower case letter
secondsecond
TT
tt
TT
tt
=>
=>
=>=> TT TT TT tt
T tT t t tt t
Probability Can be determine by completing a Can be determine by completing a Punnett Punnett
SquareSquare . . Example:Example:
X Y
X XX XY
X XX XY
1/2
Probability of first offspring being a male:
What are the chances of having a boy?What are the chances of having a boy?
Probability Probability Probability does not changedoes not change after traits show after traits show
up in an offspring. up in an offspring. Same chanceSame chance still exists for every possibility still exists for every possibility
of being expressed.of being expressed.X Y
X XX XY
X XX XY
Probability of first offspring being a male: 1/2
Probability of second offspring being a male:
Probability of third offspring being a male:
1/2
1/2
Probability Ratios Probabilities Probabilities predictpredict the average outcome of the average outcome of
a large number of events a large number of events Probability can be expressed as a ratio, Probability can be expressed as a ratio,
fractionfraction, or percent, or percent A ratio is a A ratio is a proportionproportion
It It compares quantitiescompares quantities relative to each relative to each otherother
The The largerlarger the the samplingsampling of individuals, the of individuals, the closercloser the the ratioratio will be to the predicted ratio will be to the predicted ratio
Genetic Ratios Comparing the number of genotypes or Comparing the number of genotypes or
phenotypes of the possible offspringphenotypes of the possible offspring Genotypic RatioGenotypic Ratio
Comparing the Comparing the amountamount of offspring that of offspring that express express each allele combinationeach allele combination in a given in a given crosscross
Phenotypic RatioPhenotypic RatioComparingComparing the amount of offspring that the amount of offspring that
express each express each physical traitphysical trait in a given in a given crosscross
Example Genotypic RatioGenotypic Ratio
There is one homozygous There is one homozygous dominant, two heterozygous, dominant, two heterozygous, and one homozygous and one homozygous recessive.recessive.
The ratio is 1:2:1The ratio is 1:2:1 1BB:2Bb:1bb1BB:2Bb:1bb
Phenotypic RatioPhenotypic Ratio There are three brownsThere are three browns
and one green. and one green. The ratio is 3:1The ratio is 3:1 3brown:1green3brown:1green
brown green
The Punnett Square Lets do a punnett square
Trait- skin of pea seeds (smooth or wrinkled)
Alleles- S= smooth and s= wrinkled
SS Ss
Ss ss
Smooth Smooth
Smooth Wrinkled
Ss X Ss
Punnett Square ExamplePure Smooth X Pure DentedMendel’s Traits in Pea Plants
2 Heterozygous Smooth Crossed
Mendel’s Work Observed several traits
Height: Tall (T) and Short (t) Mated Pure Tall (TT) plants with short (tt)
plants Called Parent “P” generation
Offspring were always tall Called offspring “F1”
generation F = Filius =
t
t
T T
TtTt
Tt TtSON!
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 t
ttTt
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
F
F
f
f
FF Ff
Ff ff
Father’s Genes
Mother’s Genes
Ff x Ff
The Punnett Square What are the genotypes of offspring with free What are the genotypes of offspring with free
earlobes?earlobes? If the genotype is ff, what will the phenotype If the genotype is ff, what will the phenotype
be?be? Genotype Ratio:Genotype Ratio:
F
F
f
f
FF Ff
Ff ff
FFFF and FfFf
Attached Attached earlobesearlobes 1FF : 2Ff : 1ff1FF : 2Ff : 1ff
The Punnett Square How many offspring will have free
earlobes? How many will have attached earlobes?
F
F
f
f
FF Ff
Ff ff
Mother’s Genes
Father’s Genes
3
1
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? What phenotypes will
the offspring have andhow many will therebe?
2/4 cleft chin 2/4 smooth chin
I
i
i
i
Ii
Ii ii
ii
Ii, ii