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Genetics and Probability: Understanding Mendel's Laws

Explore how Mendel's laws of segregation and independent assortment in genetics mirror the laws of probability applied in coin tosses and dice rolls. Learn about calculating gamete probabilities and how to apply rules of multiplication and addition. Understand dihybrid crosses and the Chi-square test in genetics.

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Genetics and Probability: Understanding Mendel's Laws

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  1. Probability & Genetics

  2. Genetics & Probability • Mendel’s laws: • segregation • independent assortment reflect same laws of probability that apply to tossing coins or rolling dice

  3. P P P p PP Pp 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… 50% 100%

  4. P p Pp Probability & genetics • Outcome of 1 toss has no impact on the outcome of the next toss • probability of tossing heads each time? • probability making a P gamete each time? 50% 50%

  5. male / sperm P P PP P p P p p P p p Pp pp P female / eggs p Calculating probability Pp x Pp sperm egg offspring 1/2 x 1/2 = 1/4 1/2 x 1/2 = 1/4 PP Pp 1/2 x 1/2 = 1/4 1/2 Pp pp 1/2 x 1/2 = 1/4

  6. 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 x Pp  pp 1/2 x 1/2 = 1/4 1/2 x 1/2 = 1/4

  7. Product law • For simultaneous outcomes (AND) • What is the chance that you will roll snake eyes with two dice? (1 and 1) • Chance of rolling 1 with first die = 1/6 • Chance of rolling 1 with second die = 1/6 • Chance of rolling two 1’s = 1/6 X 1/6 = 1/36 • We used product law when calculating probabilities by the forked-line method.

  8. Calculating dihybrid probability • Rule of multiplication also applies to 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

  9. P p Pp sperm egg offspring p P Pp 1/2 x 1/2 = 1/4 1/4 1/4 + 1/2 x 1/2 = 1/4 1/2 Rule of addition • Chance that an event can occur 2 or more different ways • sum of the separate probabilities • probability of Pp x Pp  Pp

  10. Sum law • For outcomes that can occur more than one way (OR) • What is the chance that you will roll either a 1 or a 6 with one die? • Chance of rolling 1 = 1/6 • Chance of rolling 6 = 1/6 • Chance of rolling 1 or 6 = 1/6 + 1/6 = 2/6 = 1/3

  11. Chi-square test • Test to see if your data supports your hypothesis • Compare “observed” vs. “expected” data • is variance from expected due to “random chance”? • is there another factor influencing data? • null hypothesis • degrees of freedom • statistical significance

  12. Any Questions??

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