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## Tossing Coins

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**Section 11-2**Interest Grabber Tossing Coins • If you toss a coin, what is the probability of getting heads? Tails? If you toss a coin 10 times, how many heads and how many tails would you expect to get? Working with a partner, have one person toss a coin • ten times while the other person tallies the results on a sheet of paper. Then, switch tasks to produce a separate tally of the second set of 10 tosses. Go to Section:**Interest Grabber continued**Section 11-2 1. Assuming that you expect 5 heads and 5 tails in 10 tosses, how do the results of your tosses compare? How about the results of your partner’s tosses? How close was each set of results to what was expected? 2. Add your results to those of your partner to produce a total of 20 tosses. Assuming that you expect 10 heads and 10 tails in 20 tosses, how close are these results to what was expected? 3. If you compiled the results for the whole class, what results would you expect? 4. How do the expected results differ from the observed results? Go to Section:**Section 11-2**Section Outline • 11–2 Probability and Punnett Squares A. Genetics and Probability B. Punnett Squares C. Probability and Segregation D. Probabilities Predict Averages Go to Section:**Genes and Physical Traits**• Genotype – genetic makeup of alleles • Geno = “genes” • Ex: AA, Aa or aa; dominant or recessive, heterozygous or homozygous • Phenotype– physical expression of traits or what organism looks like! • Pheno = “to show” • Ex: tall or short, green or yellow, blue eyes or brown eyes**Genotypes and Phenotypes are different.**TALL TALL • All tall plants have the same phenotype, or physical characteristic of tallness. • They do not, however, have the same genotype, or genetic makeup (alleles!) • Same phenotype but different genotype. **Determining Genotypes and Phenotypes.**TALL TALL • Can we know phenotype if we know the genotype? • Why? • Can we know the genotype if we know the phenotype? • Why not?**Checkpoint**• What are different forms of the same gene called? • For genotype TT, is this dominant or recessive? Homozygous or heterozygous? • What is the phenotype of a heterozygous plant if purple flowers dominate white flowers? ANY QUESTIONS?**KEY CONCEPT Genes encode proteins that produce a diverse**range of traits.**What is homozygous?**Having two identical alleles for a trait. Homozygous Dominant – two dominant alleles = AA Homozygous Recessive – two recessive alleles = aa What is heterozygous? Having two different alleles for a trait. = Aa**The same gene can have many versions.**• A gene is a piece of DNA that directs a cell to make a certain protein. • Each gene has a locus, aspecific position on a pair ofhomologous chromosomes.**An allele is any alternative form of a gene occurring at a**specific locus on a chromosome. • Each parent donates one allele for every gene. • Homozygous describes two alleles that are the same at a specific locus. • Heterozygous describes two alleles that are different at a specific locus.**Genes influence the development of traits.**• All of an organism’s genetic material is called the genome. • A genotype refers to the makeup of a specific set of genes. • A phenotype is the physical expression of a trait.**Alleles can be represented using letters.**• A dominant allele is expressed as a phenotype when at least one allele is dominant. • A recessive allele is expressed as a phenotype only when two copies are present. • Dominant alleles are represented by uppercase letters; recessive alleles by lowercase letters.**Both homozygous dominant and heterozygous genotypes yield a**dominant phenotype. • Most traits occur in a range and do not follow simple dominant-recessive patterns.**KEY CONCEPT The inheritance of traits follows the rules of**probability.**What is probability?**• The likelihood that an event will occur. Usually expressed in a ratio. • Probability can be used to predict the outcome of genetic crosses. • What is a Punnett Square? • A diagram that shows the segregation of genes.**Probability and Punnet Squares**• Whenever Mendel crossed two hybrid plants (F1), he got 3:1 ratio or ¾ dominant and ¼ recessive. • Mendel realized that the principles of probability (MATH!!) could be used to explain the results of genetic crosses.**Genetics and Probability**Probability - the likelihood that any particular event(s) will occur • Ex: coin flip – probability of heads is 1 chance out of 2 possible outcomes = 1/2, or 50%. • Does heads on the first flip change the probability of heads on the next? What if heads 10 times in a row – will next flip be more likely tails? Past outcomes do not affect future ones**Genetics and Probability**What is the probability that we will flip heads three times in a row? Because each event is independent : (probability of event)N = number of events or ½ x ½x ½ = (½)3 = 1/8 1 in 8 chance that 3 heads flipped in a row**Genetics and Probability**How is this related to genetics? Allele segregation is equally random and each event independent. Chances of inheriting a given allele from a heterozygous parent = 50% or 1/2 If parent, T or t – you have a 50% chance of either, same as heads or tails**Probability and Gender**Females = homozygous XX What is the probability that you will inherit an X from your mother? Males = heterozygous XY. What is the probability that you will inherit an X from your dad? Probability of a Y? What is the probability of having a boy? Having a girl? Which parent’s genes determine your gender? What is the probability that a family with three children will have all girls? (probability of event)N = number of events ½ x ½x ½ = (½)3 = 1/8**Checkpoint**• What does probability mean? • Given that you have a 50% chance of having boy, what is the probability that your second child will be a boy if your first is girl? • What is the probability that a family of four will be all girls? ANY QUESTIONS?**Why Punnett squares?**• Predicts the probability of a cross between two organisms. • Rules: • Dominant allele represented by a Capital letter (T for tall) • Recessive allele represented by a lower case letter (t for short) • The letters designate the two forms of one gene, the two alleles for a monohybrid cross. • Every cell in your body has at least two alleles for every trait, one from Mom and one from Dad)**Punnett squares illustrate genetic crosses.**• The Punnett square is a grid system for predicting all possible genotypes resulting from a cross. • The axes representthe possible gametesof each parent. • The boxes show thepossible genotypesof the offspring. • The Punnett square yields the ratio of possible genotypes and phenotypes.**Punnet Squares**Punnett square – grid showing possible gene combinations for offspring from a given genetic cross. • predicts genetic variations and their probability • Shows phenotype & genotype ratios**PUNNETT SQUARE**Parents gametes Offspring**Setting up a Punnett Square**• Determine Parent genotype. • Capital for dominant, lower case recessive. • Top and left letters = divide parent alleles • Bring down from top and over from left to create possible genotype combinations for offspring. Short plant x Tall heterozygote Tt Tt tt tt**Checkpoint**We crossed a heterozygous black female with a white male. What is the genotype of the female? The male? Draw punnett square for this cross. Black (B) hair dominates white (b) in guinea pigs. B b b Bb bb b Bb bb**Ratios and Punnett Squares**Genotype ratio – number of each type of offspring genotype predicted by punnett square • For a single trait (monohybrid cross) – homozygous dominant: heterozygous: homozygous recessive #TT : #Tt : #tt Phenotype Ratio – number of each type of offspring phenotype predicted by a punnett square dominant:recessive traits #Tall : #short**Monohybrid Cross:**• Provided data for one pair of contrasting traits. • What are the possible genotypes that can result? • What are the possible phenotypes that can result? • What is the ratio of tall to short plants in a hybrid cross? • Does this ratio agree with Mendel’s result in the F2 generation?**A monohybrid cross involves one trait.**• Monohybrid crosses examine the inheritance of only one specific trait. • homozygous dominant-homozygous recessive: all heterozygous, all dominant**heterozygous-heterozygous—1:2:1 homozygous dominant:**heterozygous:homozygous recessive; 3:1 dominant:recessive**heterozygous-homozygous recessive—1:1**heterozygous:homozygous recessive; 1:1 dominant:recessive • A testcross is a cross between an organism with an unknown genotype and an organism with the recessive phenotype.**Checkpoint**How many piglets are homozygous dominant? Heterozygous? Homozygous recessive? What is the genotype ratio? How many black? White? What is the phenotype ratio? Black (B) hair dominates white (b) in guinea pigs. B b b bb Bb b Bb bb ANY QUESTIONS?**A dihybrid cross involves two traits.**• Mendel’s dihybrid crosses with heterozygous plants yielded a 9:3:3:1 phenotypic ratio. • Mendel’s dihybrid crosses led to his second law,the law of independent assortment. • The law of independent assortment states that allele pairs separate independently of each other during meiosis.**Law of Independent Assortment**• genes for different traits can segregate independently during the formation of gametes. • Independent assortment = genetic variation • Mendel concluded that the inheritance of one trait does notinfluence the inheritance of a second trait**Independent Assortment occurs in Meiosis – Metaphase I**r = wrinkled R = round R r R Y = yellow y = green y Y r R R r Y y y Y r r R R R R r r Y Y y y Y Y y y**Probability =**number of ways a specific event can occur number of total possible outcomes Heredity patterns can be calculated with probability. • Probability is the likelihood that something will happen. • Probability predicts an average number of occurrences, not an exact number of occurrences. • Probability applies to random events such as meiosis and fertilization.**Probability and Punnett Square**• Probabilities predict averages, not exact outcomes • Probability is more accurate when you have more chances**Exploring Mendelian Genetics**• Because organisms are made up of more than one trait, Mendel wondered if they sort independently. • For example, does the gene that determines whether a seed is round or wrinkled in shape have anything to do with the gene for seed color? • Must a round seed also be yellow?**DIHYBRID CROSS**Crossing organisms with genes for two different traits = 2X as many possible gametes. If we cross RRYY with rryy – what are the possible gametes?**DIHYBRID CROSS : punnett square for true breeding or**homozygous parents. R = round r = wrinkled Y = yellow y = green**DIHYBRID CROSS**What possible gametes do we get from crossing RrYy and RrYy?**DIHYBRID CROSS**What possible gametes do we get from crossing RrYy and RrYy? Ry rY ry RY RY Ry rY ry**heterozygous**Offspring have combinations of alleles not found in earlier generations = alleles segregated independently**DIHYBRID CROSS**Classic phenotype ratio from dihybrid cross of heterzygotes = 9:3:3:1**Summary of Mendel’s Principles**• Traits come from your inherited genes. • Genes may have more than one allele and some are dominant. • Your two copies of each gene (one from each parent) are segregated or separated when gametes form. • Alleles for different genes usually segregate independently of one another.**Checkpoint**Black (B) hair dominates white (b) Long (L) dominates short(l) We crossed a female heterozygous for both long black hair with a short, white haired male. What is the genotype of the female? The male? What are the possible gametes for the female? What are the possible gametes for the male? Draw the dihybrid punnett square for this cross. ANY QUESTIONS? 48**BbLl**• BL • Bl • bL • bl