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Transcript
It’s Probably Probability
By Virginia V. Lewis
NSF Scholar
1
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
2
Let’s Play!
• Pick a three-digit
number. Record your
number on your class
notes.
• Hope you’re feeling
lucky
3
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
4
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.
5
Chip Activity
6
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.
7
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?
8
Card Activity
9
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?
10
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……
11
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.
12
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
13
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
14
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.
15
Mother’s
Chromosomes
Father’s
Chromosomes
Sample Space
X
X1X
Y
X1Y
X1
X2
X
X2X
Y
X2Y
16
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.
17
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.
18
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.
19
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.
20
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.
21
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
22
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.
24
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
25
Practice #4b
• Now try making a Tree Diagram for this
situation.
• What is the probability I will have freckles?
26
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
27
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!!!!!!!!!!!!!!!!!!!!!!
28