How to solve genetics problems using Binominal Expansion Formula

Same problem alternative metod of solving: How to solve Probability Problems in Genetics using Factorial Method Binomial Expansion Assume that a couple plans to have five children. In this case, it is somewhat tedious to outline and then calculate all the possible combinations because the number of independent events has increased beyond three or four. Fortunately, if one knows the number of events and the individual probabilities of each alternative event, the probabilities of various combinations can be calculated directly using binomial expansion. For a hypothetical couple that plans to have one child, boy is one possible outcome (and we call that a) and girl is the other alternative (and we call that b). Because boy or girl is equally likely (and equal to ½), the total probability of having a boy or girl is a b = 1. For a couple interested in two children, we simply calculate (a b)(a b) = 1, or (a b)2 = 1. Expanding this gives: a2 2ab b2 = 1. Probability of two boys: a2 = (½)2 = ¼ Probability of one boy, one girl: 2ab = 2(½)(½) = 2/4 = ½ Probability of two girls: b2 = (½)2 = ¼ Total: 1 Generally, the formula for binomial expansion is (a b)n, where n equals the number of independent events. (Your text, P-108, shows how to set up a simple table for determining the coefficients.) For example, if four children were planned, the expansion would appear thus: (a b)4 = a4 4a3b 6a2b2 4ab3 b4 This can be interpreted as indicating that there are 4 ways to get three boys and one girl, 4a3b (and, likewise, to get one boy and 3 girls, 4ab3), 6 ways to get 2 boys and 2 girls (6a2b2), etc. The terms in this binomial expansion show directly that the probability of 4 boys is: a4 = (1/2)4 = 1/16 Similarly, the probability of 3 boys and 1 girl is: 4a3b = 4(1/2)3(1/2) = 4/16 1. Complete the rest of the combinations to be sure you understand this. 2. Let’s return to the couple interested in five children. Use binomial expansion to calculate the probability of having five boys; four boys and one girl; and all the other combinations. Complete your work on the back of the Probability Worksheet and hand this in before you leave lab. #heterozygotic #chromatin #Iherb #PascalsTriangle #chromatid #GeneticsExamQuestionsSolutions #recessive #Genetics #DNA #genes #meiosis #transcription #equation #gene #geneExpression #genotype #GeneticExamQuestionsSolutions #cytosine #adenine #Anaphase #protein #centromere #bloodType #CellCulture #nucleicAcid #chromosome #Eukaryotic #geneticCode #RnaSplicing #AllelicFrequencies #binomialExpansion #GeneticsLecture #aminoAcid #centromeres #Genetics101 #Cancer #punnettSquare #enzyme