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