GEN 3000 Notes Set 5 01 152016 Dr Tsai Clemson University Chapter 3 Continued Reminder The multiplication product rule is used any time you are asking AND where you have independent events and you want to figure out the probability of these events happening one after the other Probability Can be applied to hybrid dihybrid or even greater crosses The easiest way to work with probability in larger crosses is by looking 1 loci at a time In other words when looking at RrYy x RrYy only look at the R s first then the Y s o How likely is it the offspring will have the genotype rryy First we look at the R loci In parent 1 there is a chance to get the r which is the same as parent two Since we re looking for r AND r we must multiply the two probabilities together x chance of getting an rr o If we look at the Y loci there is a chance to get the y out of both parents allowing us to do the same process of x chance of getting y AND y o However we need to get rr AND yy Since we need both of these combinations we must multiply the probability of each loci occurring which we just found as follows x 1 16 chance to get the genotype of rryy o What about this example Probability of crossing RRYy x RrYy to get RrYy Answer and work is below in white highlight and change color to see Probability of R s Parent 1 2 2 or 1 chance of an R Parent 2 Probability of Y s Parent 1 chance of a Y Parent 2 chance of chance of an r 1 x a y x chance of a Yy Probability of genome in question chance of Rr chance of Yy We need both so x 1 8 chance of RrYy o NOTE This is probability of genotypes When looking at the probability of phenotypes we will take other factors into account This is easier to understand once you know how to use the addition rule which can be found below inheritance We can relate Mendel s pea plants to chromosomes and the overall idea of independent Walter Sutton 1900s Studied insects and discovered that chromosome sets contain one chromosome from the maternal side and one from the paternal side He also found that these chromosome sets segregate independently at meiosis He developed the Chromosome Theory of Heredity from this the idea that genetic material in all living organisms is contained in chromosomes Each homologous chromosome has corresponding alleles The two alleles segregate during either anaphase I or anaphase II depending on whether or not crossing over has occurred The addition Rule of probability When two mutually exclusive events are connect by an either or an or we must use the addition rule In other words if two evens can happen separately and do not rely on each other we must add the probability of each individual event happening together If we are wondering what the probability of getting heads OR tails of a coin flip we would take 1 or 100 If we look at a die and we want to see what the probability of rolling a EITHER a two OR a three is we look at each one We know with 6 sides the probability of rolling a two is a 1 6 as is the probability of rolling a three a 1 6 Since we re using the addition rule we must add them together to get 1 6 1 6 2 6 NOTE 2 6 can then be simplified to 1 3 ALL FRACTIONS SHOULD BE SIMPLIFIED We can apply the addition rule to genetics very easily If we look at a cross of Tt x Tt and we want to know how likely it is to get the dominant gene expressed we can use probability to figure that out o We know if a dominant gene is expressed it has to have at least 1 dominant allele but can also have a recessive allele That means we might have TT tT or Tt genotype to get an offspring expressing the dominant trait We know from a Punnett square that there is a chance of a TT a chance of tT a chance of Tt and even though we won t be using it in this case a chance of a tt o To see how probable it is for a dominant expressive offspring in other words to have TT OR tT OR Tt we add their individual probabilities together chance of having a dominant expressing offspring This can also be done with more loci as well o What about this example Tt x Tt what is the probability of the offspring having either a Homozygous dominant or a homozygous recessive offspring without using the Punnett square Answer and work below in white highlight and change color to see Chance of getting T from both parents chance from parent 1 and chance from parent 2 so x chance of a dominant T from both parents to get a TT offspring Chance of getting t from both parents chance from parent 1 and chance from parents 2 so x chance of a recessive t from both parents to get a tt offspring Chance of TT OR tt The OR indicates we must use addition chance of getting a TT OR tt We can use both the multiplication and addition rule within the same probability to determine the chances of a certain phenotype or genotype occurring as can be seen in the extra example above Harder example using both the addition and multiplication rules What is the probability that AaBbCC x aaBbCc will give us an offspring recessive for a OR an offspring recessive for b Remember in order for a trait to be recessive it HAS to have TWO recessive alleles In other words the offspring must have two a s or two b s Chance of getting an a from BOTH parents parent 1 has chance of an a parent 2 has 2 2 chance or 1 for an a So to get a AND a we take x 1 chance of an aa genotype Chance of getting a b from BOTH parents Parent 1 has chance of a b Parent 2 has chance of a b as well So to get b AND b we take x chance of a bb genotype Chance of getting aa OR bb Because the example is asking for the likelihood of either recessive a or recessive b we must use addition We have chance of an aa genotype and chance of a bb genotype 3 8 chance of a recessive expression in a or b alleles What if it was the chance of getting recessive a and recessive b expression Answer to the right in white highlight and change color to see x 1 8 chance of both aa and bb genotypes Chance In the real world things do not always happen according to probability There is always a measure of chance involved For instance if you …