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 Event outcome Question Event Heads or tails? The flip Heads

Probability example (contd.) Question Event Event outcome Heads The flip Heads or tails? Probabilities 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) 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

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 Male across the top Female down the side Sperm => <= Egg

The Punnett Square If we cross two heterozygous tall Tt x Sperm possibilities Egg possibilities Tt T t Sperm => <= Egg T t

The Punnett Square Offspring (diploid zygote) possibilities go inside the boxes Bring 1 letter down Bring 1 letter over Capital letter first Lower case letter second T t => T => T T T t t T t t t

Probability Can be determine by completing a Punnett Square . Example: XX XY What are the chances of having a boy? Probability of first offspring being a male: 1/2

Probability Probability does not change after traits show up in an offspring. Same chance still exists for every possibility of being expressed. X Y XX XY Probability of first offspring being a male: 1/2 Probability of second offspring being a male: 1/2 Probability of third offspring being a male: 1/2

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 Genotypic Ratio Phenotypic Ratio brown green 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 Ss Smooth Smooth Ss ss Smooth Wrinkled

Punnett Square Example Mendel’s Traits in Pea Plants Pure Smooth X Pure Dented 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 Tt Tt t SON! t 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 TT Tt T t Tt tt

Working with Punnett Squares 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 Ff x Ff F f FF Ff Mother’s Genes F ff f Ff

The Punnett Square What are the genotypes of offspring with free earlobes? If the genotype is ff, what will the phenotype be? Genotype Ratio: FF and Ff Attached earlobes 1FF : 2Ff : 1ff F f FF Ff F ff f Ff

The Punnett Square How many offspring will have free earlobes? How many will have attached earlobes? 3 1 Mother’s Genes F f FF Ff Father’s Genes F ff f 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 i Ii i ii ii Ii i Ii, ii 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 and how many will there be? 2/4  cleft chin 2/4  smooth chin Ii, ii I i Ii i ii ii Ii i