Transcript Probably Probability

It’s Probably Probability
By Virginia V. Lewis
NSF Scholar
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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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Let’s Play!
• Pick a three-digit
number. Record your
number on your class
notes.
• Hope you’re 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
• 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.
Is this situation
an example of
independent or
dependent
events?
What is the
probability that
she pulled out
twenty-six cents?
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Card Activity
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Practice #3
 Calculate the
theoretical probability
of drawing out a spade
and then another spade
with and without
replacing the first
card.
How is this
theoretical probability
related to the
experimental
probability the class
determined?
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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?
• Let’s 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
• On the left side we put
the traits of the mother
and on the top we put
the traits of the father.
Father’s Chromosomes
Mother’s Chromosomes
• Punnett squares are
used to determine the
possibilities of
inheritance when a
male and female
reproduce.
X Y
X
X
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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.
• How many of these
possibilities will be
male children? Female?
• What is the probability
of a child being male?
Female?
X Y
X1
X1X X1Y
X2
X2X X2Y
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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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Mother’s
Chromosomes
Father’s
Chromosomes
Sample Space
X
X1X
Y
X1Y
X1
X2
X
X2X
Y
X2Y
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Probability of Gender
 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?
Determine the
probability that if a
family has two children
they both will be male.
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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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Let’s Use the Punnett Square
Mother’s Genotype
Father’s Genotype
b
b
B Bb Bb
b bb bb
• 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
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eyes.
Now Using a Tree Diagram!
Mother’s
Genotype
Father’s
Genotype
Sample Space
b
Bb
b
Bb
B
b
b
bb
b
bb
Wow!
The
results
are the
same. I
still have
a 50%
chance of
having
Brown
eyes. 23
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 mother’s genotype
is FF and my father’s
genotype is ff.
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The Solution
Mother’s Genotype
Father’s 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
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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
Mother’s
Genotype
Father’s
Genotype
Sample Space
Ff
f
The same
results!!!
F
Ff
f
F
f
Ff
f
Ff
I will
definitely
have
freckles
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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 let’s play!!!!!!!!!!!!!!!!!!!!!!
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