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# Lec 5 Bio 308 Bio 308

NIU

GPA 2.9

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This 3 page Class Notes was uploaded by Kiara Reyes on Monday September 5, 2016. The Class Notes belongs to Bio 308 at Northern Illinois University taught by M. Johns in Summer 2016. Since its upload, it has received 4 views. For similar materials see Genetics in Biology at Northern Illinois University.

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Date Created: 09/05/16

Lecture 5: Probability Probability- what is the chance that a given event will occur? Ex] What is the chance that a child, or a family of children, will have a given phenotype? Probability is expressed in numbers between 0 and 1 0= event never happened 1= event always happened Probability of an event equals the number of times it happens divided by the number of opportunities Ex] Rolling a die (singular of dice) The chance of rolling a 2 is 1/6, because there is a 2 on one face and a total of 6 faces “AND Rule of Probability” Probability of 2 independent events both happening is the product of their individual probability; “this event happens AND that even happens” Ex] what is the probability of rolling a 2 on one die and a 2 on a second die? -For each event 1/6, both probability is 1/6 times 1/6 equals 1/36 Event have to be independent: they can’t affect each other’s probability of occurring Ex] You have a hat with a red ball and green ball in it. Probability drawing out the red ball is 1/2, same chance as the green ball. Once drawing one of the ball the other ball is 1 while the chosen ball is 0 “OR Rule of Probability” Probability that either one of 2 different event will occur is the sum of their separate probability Ex] chance of rolling either 2 or 3 on a die is 1/6 plus 1/6 equals 1/3 “NOT Rule” The chance of an event not happening is 1 minus the chance of it happening Sometimes complicated problems are greatly simplified examining the background Ex] Chance of not getting 2 on a die is 1minus 1/6 equals 5/6 “Combining the Rules” More complicated situation involve combining the AND and OR rules Important to keep track of the individuals involved and not allow them to be confused Probability and Genetics The probability that any individual child has a certain genotype is calculated using Punnett Square Interested in calculating the probability of a given distribution of phenotype family of children “Sex Ratio in a Family of 3” Assuming that the probability of a boy= ½ and girl= ½ Enumerate each child separately for each of the 8 possible families 1/8 ( ½* ½* ½*) and 1/8+1/8+1/8= 3/8 “Different Probability for Different Phenotype” Family of 3 children, but this time parents are heterozygous for Tay- Sachs, a recessive genetic disease -3/4 chance being normal (TT or Tt) -1/4 chance having the disease (tt) -Chance of all 3 normal= 27/64 -Chance of all 3 with disease= 1/64 -1 normal + 2 disease= 3/64+ 3/64+ 3/64= 9/64 -2 normal + 1 disease= 27/64 -3 normal= 27/64 -Sum= 9/64+ 27/64 + 27/64= 63/64 This could be done with the NOT rule: -At least 1 normal -NOT all 3 with disease 1-1/64= 63/64 Larger Families: Binomial Distribution Basic methods of examining all possible families and counting the one of proper types gets unwieldy with big families Binomial Distribution- is a shortcut method based on the expansion of the equation => (p+q)^2= 1 (examples under) p= probability of one event (normal) q= probability of one alternative event (mutation) n= number of children in family Writing the terms of the Binomial expansion you need to get the exponents and coefficients -Exponents: vary the exponents of p and q so they always add to n -Coefficients: using the Pascal’s Triangle Now applying the coefficient to the terms

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