Biology and Chance

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Biology and Chance

• JP Slovak

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Importance of knowing probability if you want to
study biology.

• Formation of gametes
• Understanding mutation
• Understanding Evolution
• Statistical analysis of data
• Risk assessment

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Some Basics
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Calculating a probability

• P(E) number of outcomes contained in the event
  / total number of outcomes in the sample space
• Example If you roll a die once what is the
  probability you roll a number greater than 4.
• P(E) 25,6/61,2,3,4,5,6 1/3

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Empirical probability
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The Rules

• The probability of an event must be between 0 and
  1.
• 1 is certain
• 0 is impossible
• The sum of the probabilities of all possible
  outcomes of a sample space is equal to 1.
• Ex. All the possible outcomes of a monohybrid
  cross. Aa x Aa. AA .25 Aa .5 aa .25
• .25 .5.25 1

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The Rules

• The probability that a event will not occur is
  equal to 1 minus the probability that the event
  will occur.
• Ex. The chance of rolling a six on a single row
  is 1/6 so the chance of not rolling a six is 1
  1/6 5/6.
• This is the Complement rule

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The Rules

• The addition rules
• P(A or B) P(A) P(B)
• If you roll a die once, find the probability of
  getting a 1 or a 2.
• If you have a group of 6 freshmen, 10 sophomores
  and 4 juniors, find the probability that a
  randomly selected individual from this group is a
  freshman or sophomore.
• Use this rule when events are mutually exclusive.

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The Rules

• The addition rules
• 2. P(A or B) P(A) P(B) P(A and B)
• If you have a standard deck of cards, find the
  chance you will draw a heart or a 4.
• It is possible for a heart and a 4 to occur
  together. That probability would be 1/52.
• Use this rule when events are not mutually
  exclusive.

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Venn Diagram


36 other cards
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The Rules

• The Multiplication Rules
• P(A and B) P(A) P(B)
• If you toss a coin and roll a die, find the
  probability of getting a head on the coin and a
  five on the die.
• Use this when the two events are independent.

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The Rules

• Multiplication Rules
• 2. P(A and B) P(A) P(BA)
• Ex. You have a box of 7 parts, 3 of which are
  defective. You will not put a defective part
  back in the box. What are the chances that the
  first two parts you choose are defective.
• Use this rule when events are dependent.
• Without replacement.

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The Rules

• The Counting Rules
• Combinations

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The Rules

• The Counting Rules
• Permutations

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The Binomial model

• Used in many processes throughout biology and the
  sciences in general
• Conditions for proper use of the binomial
• Fixed number of trials
• You can classify the outcome in two ways
• The probability of success is the same for each
  trial
• The trials are independent

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The Binomial
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The Binomial
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The Binomial

• Expected Value
• Expected value np
• Standard Deviation
• SD

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The Binomial

• If you have 20 offspring from a monohybrid cross,
  calculate the expected value and standard
  deviation for the number of homozygous
  recessives.

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The Binomial

• Suppose that plants with genotype BB and Bb are
  tall with the recessive (bb) being short. If we
  cross two heterozygotes, according to classical
  genetics, ¼ of the resulting offspring should be
  short. The plant produces eight offspring. What
  is the probability that exactly two are short.

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The Binomial

• Does this scenario meet the conditions for
  appropriate use of the binomial?
• What is n?
• What is r?
• What is p?

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We come into the world and take our chances Fate
is just the weight of circumstances Thats the
way that lady luck dances Roll the bones -Rush