It

1
Its Probably Probability

• By Virginia V. Lewis
• NSF Scholar

2
How do you play Pick 3?

• There are three containers. Each container has
  10 balls in it labeled from 0 to 9.
• The player picks a three-digit number.
• If all three digits match in the correct order,
  you win 500

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Lets Play!

• Pick a three-digit number. Record your number on
  your class notes.
• Hope youre feeling lucky?

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Important Terms
Probability the likelihood that an event will
occur
If the sample space is limited in size. A
Probability of

• 1 - implies the event is guaranteed to happen
• 0 implies the event is impossible
• .5- implies the event has a 50
  percent chance of occurring

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Independent vs. Dependent Events

• Sometimes the outcome of an event will affect the
  next event and sometimes it will not.
• Independent events are two events where the
  outcome of the first event does not affect the
  outcome of the second event.
• Dependent events are two events where the outcome
  of the first event affects the outcome of the
  second event.

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Chip Activity
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Practice 1

• Each letter of the word Lucky is written on a
  separate slip of paper. The five slips of paper
  are placed in a paper bag and two slips are drawn
  at random. The first letter is replaced before
  the second letter is drawn.

• Is this problem an example of independent or
  dependent events?
• Find the probability the first letter is L and
  the second letter is k.

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Practice 2

• Is this situation an example of independent or
  dependent events?
• What is the probability that she pulled out
  twenty-six cents?

• Shae has four coins in her pocket. She has a
  dime, one penny, a nickel, and a quarter.
• Shae needs twenty-six cents to pay the cashier.
  She reaches in her pocket and takes out two coins.

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Card Activity
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Practice 3

• How is this theoretical probability related to
  the experimental probability the class
  determined?

• Calculate the theoretical probability of drawing
  out a spade and then another spade with and
  without replacing the first card.

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Probably Hereditary

• Probability plays an important role in the area
  of genetics.
• What do you think the probability is that a child
  about to be born will be male?
• What if the mother already has two boys? Three
  boys?
• Lets take a look at the genetics and see

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Basic Genetics

• When we are born we have one chromosome from our
  mother and another chromosome from our father.
• If you are a girl than your chromosomes are XX
  and if you are a boy then your chromosomes are XY.

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Punnett Squares
Fathers Chromosomes

• Punnett squares are used to determine the
  possibilities of inheritance when a male and
  female reproduce.
• On the left side we put the traits of the mother
  and on the top we put the traits of the father.

X Y
X
X
Mothers Chromosomes
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Now we take one chromosome from each parent and
fill in the chart. There are four possibilities
of chromosome patterns for a new baby.
X Y
X1 X1X X1Y
X2 X2X X2Y

• How many of these possibilities will be male
  children? Female?
• What is the probability of a child being male?
  Female?

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Tree Diagram

• Tree diagrams are often used in math class to
  find the probability of an event.
• The tree diagram for the gender problem is shown
  on the next slide.

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Sample Space
Fathers Chromosomes
Mothers Chromosomes
X1 X2
X1X
X
X1Y
Y
X
X2X
Y
X2Y
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Probability of Gender

• Determine the probability that if a family has
  two children they both will be male.

• Is the birth of each child a dependent or
  independent event?
• Does the gender of the first child affect the
  gender of the second child?

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More about Heredity

• Each of us inherits an allele for a certain trait
  from each parent.
• These alleles combine to form our genotype.
• Our genotype determines our phenotype.

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My Mother

• My mother has brown eyes. Her alleles are B and
  b. Her genotype is Bb.
• Her B allele is the dominant brown eye trait.
  Her b allele is the recessive blue eye trait.
• Since she has one dominant and one recessive
  allele she has the dominant brown eye trait.

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My Father

• My father has blue eyes. His alleles are b and
  b. His genotype is bb.
• His b alleles are both recessive.
• Since he has two recessive alleles he has the
  recessive blue eye trait.

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So What About Me?

• I have one allele from my mother and one allele
  from my father.
• My genotype is determined by these alleles.
• I will have brown eyes if my genotype is BB or
  Bb.
• I will have blue eyes if my genotype is bb.

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Lets Use the Punnett Square?
Fathers Genotype

• There are four possible outcomes for my genotype.
  
• The possibilities are Bb, Bb, bb, and bb.
• Two of these four genotypes mean that I will have
  brown eyes.
• I have a 50 chance of having brown eyes.

b b
B Bb Bb
b bb bb
Mothers Genotype
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Now Using a Tree Diagram!
Mothers Genotype
Fathers Genotype
Sample Space
B b
Bb
Wow! The results are the same. I still have a
50 chance of having Brown eyes.
b
Bb
b
b
bb
b
bb
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Practice 4a

• F is the dominant allele for freckles and f is
  the recessive allele. If I have a genotype of FF
  or Ff I will have freckles. If my genotype is ff
  I will not have freckles.

• Use a Punnett square to determine the probability
  I will have freckles.

• My mothers genotype is FF and my fathers
  genotype is ff.

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The Solution
Fathers Genotype
f f
F Ff Ff
F Ff Ff

• I have four possible genotypes. But they are all
  the same, Ff.
• I have a 100 chance that I will have freckles.
• Guess I better stay out of the sun?

Mothers Genotype
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Practice 4b

• Now try making a Tree Diagram for this situation.
• What is the probability I will have freckles?

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The Solution
Mothers Genotype
Fathers Genotype
Sample Space
F F
Ff
f
The same results!!! I will definitely have
freckles?
Ff
f
f
Ff
f
Ff
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Back to Pick 3

• Is the Pick 3 Game an example of independent or
  dependent events?
• Use your new knowledge of probability to
  determine the likelihood of winning 500 in Pick
  3.
• Now lets play!!!!!!!!!!!!!!!!!!!!!!