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Lecture

# Probability and Punnett Squares.docx

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School
Department
Biology
Course
BIOLOGY 2C03
Professor
Bhagwati Gupta
Semester
Fall

Description
September 10 , 2013 Biology 2C03: Genetics Probability & Punnett Squares What is the Probability of a Trait (SCD) Appearing in the Offspring? - From a biological point of view, we first need to know the probability of alleles being distributed to the gametes - Mendel’s Principle of Segragation: 1. Each individual organism possesses two alleles encoding a trait 2. Alleles separate when gametes are formed 3. Alleles separate in equal proportions Punnett Square SCD: β β x β β S A - Each parental allele has a ½ chance of being passed to a child - Each combination of alleles (genotype) has a ¼ probability of occurring - ¼ children are expected to have SCD - 3 genotypes are expected in the children:  ¼ β β : ½ β β : ¼ β β S S - How many phenotypes are expected in the children:  Two phenotypes  ¾ normal: ¼ SCD A Quicker Primer in Probability - Roll a die:  Probability of rolling a 6 = P(roll a 6) = 1/6  Probability of rolling an even number = P(even) = 1/6 +1/6 + 1/6 = ½  Sum rule: the probability of the occurrence of any of the several mutually exclusive events is the sum of the probabilities of the individual events (either, or) - Roll two dice:  Probability of rolling two 6’s = P(roll 2 6’s) = 1/6*1/6 = 1/36  Probability of rolling a 6 and a 4 = (1/6*1/6) + (1/6*1/6) = 1/18  Product rule: the probability of two independent events happening simultaneously is the product of their individual probabilities (and) - If diploid individuals carry two alleles, we can liken this to a flip of a coin with two sides:  Probability of flipping a head = P(heads) = ½  Probability of flipping a tail = P(tails) = ½ S A  A person is diploid (two copies of the genome), e.g. β β  During meosis, a gamete (haploid) receives just one allele  Probability of a gamete receiving β = P(β ) = ½  Probability of a gamete receiving β = P(β ) = ½ - Coin flip simulation: first few flips, probability of heads fluctuates, but given enough trials, the probability tends towards P = 0.5 - Due to biological fluctuation, this will also be true of the inheritance of alleles - Repeat this enough times and you see a normal distribution: 100 flips, most common event would be 50 heads, 50 tails. But should not be surprised to see 49:51 or 52:48 - Towards the left and right, it is much less likely to see these ratios Probability Can be Used Where One of Two Alternative Outcomes is Possible During Each of a Large Number of Trials - Example: the probability of having two boys? P= (½)(½)= ¼  The probability of having one boy and one girl must take into account that this can occur in two ways, P = (½)(½) + (½)(½) = ½  Probability of having four boys? P= 1/16  But, say a family has four boys, what is the probability that their next child will be a boy? P= ½, these are independent events Mendel’s Concept of Dominance - This 3:1 phenotypic ratio is a Mendelian ratio – for a recessive disorder - In Mendel’s st
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