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AP Biology Laws of Probability and Chi Square Probability & Genetics.

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Presentation on theme: "AP Biology Laws of Probability and Chi Square Probability & Genetics."— Presentation transcript:

1 AP Biology Laws of Probability and Chi Square Probability & Genetics

2 AP Biology Probability & Genetics  Calculating probability of making a specific gamete is just like calculating the probability in flipping a coin  probability of tossing heads? 50%  probability making a P gamete…  Outcome of 1 toss has no impact on the outcome of the next toss  probability of tossing heads each time? 50%  probability making a P gamete each time?

3 AP Biology Rule of Addition  Chance that an event can occur 2 or more different ways  SUM of the separate probabilities  Use for heterozygous possibilities  Two ways to be heterozygous: Pp or pP  Key word is “or”.  Ex: Probability of getting 2 or a 6 on the roll of a die. 1/6 + 1/6 = 2/6 = 1/3  Ex: Probability of having offspring with dominant phenotype? PP or Pp or pP ¼+ ¼ + ¼ = ¾

4 AP Biology Rule of multiplication  Chance that 2 or more independent events will occur together  probability that 2 coins tossed at the same time will land heads up  probability of pp or PP offspring  Ex: Probability of getting a head and a tail with two different coins.  ½ x ½ = 1/4  Key word is “and”

5 AP Biology Calculating Probability of Pp x Pp ½ x ½ = ¼ = PP ½ x ½ = ¼ = pp  What about Pp?

6 AP Biology Calculating Dihybrid Probability  Rule of multiplication application with Dihybrid crosses:  heterozygous parents — YyRr  probability of producing yyrr?  probability of producing y gamete = 1/2  probability of producing r gamete = 1/2  probability of producing yr gamete  = 1/2 x 1/2 = 1/4  probability of producing a yyrr offspring  = 1/4 x 1/4 = 1/16

7 AP Biology What is Chi-Squared?  In genetics, you can predict genotypes based on probability (expected results)  Chi-squared is a form of statistical analysis used to compare the actual results (observed) with the expected results  NOTE:  2 is the name of the whole variable – you will never take the square root of it or solve for 

8 AP Biology Chi-squared  If the expected and observed (actual) values are the same then the  2 = 0  If the  2 value is 0 or is small then the data fits your hypothesis (the expected values) well.  By calculating the  2 value you determine if there is a statistically significant difference between the expected and actual values.

9 AP Biology Step 1: Calculating  2  First, determine what your expected and observed values are.  Observed (Actual) values: That should be something you get from data– usually no calculations  Expected values: based on probability  Suggestion: make a table with the expected and actual values

10 AP Biology Step 1: Example  Observed (actual) values: Suppose you have 90 tongue rollers and 10 nonrollers  Expected: Suppose the parent genotypes were both Rr  using a punnett square, you would expect 75% tongue rollers, 25% nonrollers  This translates to 75 tongue rollers, 25 nonrollers (since the population you are dealing with is 100 individuals)

11 AP Biology Step 1: Example  Table should look like this: ExpectedObserved (Actual) Tongue rollers7590 Nonrollers2510

12 AP Biology Step 2: Calculating  2  Use the formula to calculated  2  For each different category (genotype or phenotype calculate (observed – expected) 2 / expected  Add up all of these values to determine  2

13 AP Biology Step 2: Calculating  2

14 AP Biology Step 2: Example  Using the data from before:  Tongue rollers (90 – 75) 2 / 75 = 3  Nonrollers (10 – 25) 2 / 25 = 9   2 = = 12

15 AP Biology Step 3: Determining Degrees of Freedom  Degrees of freedom = # of categories – 1  Ex. For the example problem, there were two categories (tongue rollers and nonrollers)  degrees of freedom = 2 – 1  Degrees of freedom = 1

16 AP Biology Step 4: Critical Value  Using the degrees of freedom, determine the critical value using the provided table  Df = 1  Critical value = 3.84

17 AP Biology Step 5: Conclusion  If  2 > critical value… there is a statistically significant difference between the actual and expected values.  If  2 < critical value… there is a NOT statistically significant difference between the actual and expected values.

18 AP Biology Step 5: Example   2 = 12 > 3.84  There is a statistically significant difference between the observed and expected population

19 AP Biology  Bozeman Chi-squared test video  BoFDqNVk&edufilter=vBrBKiVMlaMnBr dX3oXR-Q&safe=active BoFDqNVk&edufilter=vBrBKiVMlaMnBr dX3oXR-Q&safe=active  Fill in video questions

20 AP Biology Animal Behavior Chi Square WetDry Observed value Expected value55 Chi Square = Σ (O – E) 2 / E (8.9 – 5) 2 / 5 + (1.1-5) 2 / / / / 5 = 6.084

21 AP Biology 2 variable – wet and dry so 1 degree of freedom is higher than so must reject null hypothesis. Something influenced the Pill bugs.

22 AP Biology  In 2002 The distribution for Skittles is: Green: 19.7%, Yellow: 19.5%, Orange: 20.2%, Red: 20%, Purple: 20.6%.  Color distribution for M&Ms Brown15% Yellow12% Orange20% Red 13% Green 16% Blue 24%


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