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# Probability

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• pg 1
```									                         Probability
0011 0010 1010 1101 0001 0100 1011

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Corresponds to Chapter 6 in the
text
“kinda”
Basic Probability
0011 0010 1010 1101 0001 0100 1011

• Def: Probability is defined as the ratio of
favorable outcomes to total outcomes

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– notation: P(e) =    favorable
total

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– What is the probability of flipping a coin and
Terms
0011 0010 1010 1101 0001 0100 1011

• Sample Space
• P(E)

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– between 0 and 1

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Practice
0011 0010 1010 1101 0001 0100 1011

• Pg 333 (6.1, 6.3, 6.4, 6.8)

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Example 1:
0011 0010 1010 1101 0001 0100 1011

• You have six marbles in a jar. There are 2
blue, 3 red, and 1 yellow. What is the

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probability that you reach in the jar and the
marble you pull is yellow?

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0011 0010 1010 1101 0001 0100 1011

• When you flipped a coin, did you always
get half to be heads, and half to be tails?

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– Why?

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Theoretical vs. Experimental
0011 0010 1010 1101 0001 0100 1011

• Theoretical Probability:

• Experimental Probability:              1
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– What happened as we did more trials???
Practice
0011 0010 1010 1101 0001 0100 1011

• pg. 340 (6.11, 6.14, 6.18)
• Page. 348 (6.19, 6.21, 6.25)

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Compound Probability
0011 0010 1010 1101 0001 0100 1011

• And
– P( _____ and _______ )

• Or                            1
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– P( _____ or ______ )
• Conditional Probability
– P ( a b)
Terms
0011 0010 1010 1101 0001 0100 1011

• Mutually Exclusive

• Independent
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• Dependent

• Complement
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And
0011 0010 1010 1101 0001 0100 1011

• P(A and B)= P(A) * P(B)

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Or
0011 0010 1010 1101 0001 0100 1011

• P(A or B)=P(A) +P(B) – P(A and B)

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Mutually Exclusive
0011 0010 1010 1101 0001 0100 1011

• P(A and B)=0
• P(A or B)= P(A) + P(B)

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Complement
0011 0010 1010 1101 0001 0100 1011

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Conditional Probability
0011 0010 1010 1101 0001 0100 1011

• Calculate the probability of a scenario,

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– P ( a b)
• The probability of A, given B has occurred.

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• P ( a b)=
P (b a )
P (b)
Practice
0011 0010 1010 1101 0001 0100 1011

• pg. 369 (6.54, 6.58, 6.59)

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Law of Large Numbers
0011 0010 1010 1101 0001 0100 1011

• The Law of Large Numbers states, the more
trials you have, the experimental probability

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should approach the theoretical probability

• Activity 1:
• Activity 2:
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Let’s Revisit the Marble Problem
0011 0010 1010 1101 0001 0100 1011

• You have six marbles in a jar. There are 2
blue, 3 red, and 1 yellow. What is the

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probability that you reach in the jar and the
marble you pull is yellow?

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– What if I asked you to pull two marbles….
• P( yellow and blue)
P(yellow and blue)
• Does the first draw…assuming its yellow,
0011 0010 1010 1101 0001 0100 1011

affect the second.

• This is an example of independent events
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– The first outcome does not affect the probability of

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the second
• This is an example of dependent events
– The first outcome does affect the outcome of the
second probability
Activity 4
0011 0010 1010 1101 0001 0100 1011

• To Replace or Not to Replace?

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Activity 8
0011 0010 1010 1101 0001 0100 1011

• I’m on a roll!

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Back to Theory
0011 0010 1010 1101 0001 0100 1011

• Simulations are great ways of
approximating probability.

But what chance do I really  1
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have!!

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Recall
0011 0010 1010 1101 0001 0100 1011

• Probability is the favorable number of
outcomes over the sample space…that’s it!

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Example
0011 0010 1010 1101 0001 0100 1011

• Assuming gender is equally likely, what the
probability when I have more children I will

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have at least 1more girl.
– how many ways can I get 1 more girl?

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– how many possible outcomes are there?
Tree Diagram Example
0011 0010 1010 1101 0001 0100 1011

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P ( sum = 5)
0011 0010 1010 1101 0001 0100 1011

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Pascal’s Triangle
0011 0010 1010 1101 0001 0100 1011

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Next verse…same as the first!
0011 0010 1010 1101 0001 0100 1011

• What is the probability, that in the next two
children I have, at least 1 will be a girl.
Number of Ways of
Girls     getting       1
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Go back to

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0                Pascal’s Triangle.
Find the row with
three options!
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Practice
0011 0010 1010 1101 0001 0100 1011

• pg. 364 (6.47, 6.52)
• pg. 369 ( 6.58, 6.59)

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Permutation
0011 0010 1010 1101 0001 0100 1011

• A way of getting a sample space, when
order does not matter.

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– What is the probability I can randomly open a
locker, lock?
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– 1/????

– More ways!!!!—Larger sample space
• 123, 321, 213….area all different
Combination
0011 0010 1010 1101 0001 0100 1011

• A way of getting a sample space, when
order does matter.

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– I have 5 students, I want to choose 2 at a time.
How many groups can I choose?

– Smaller sample size

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Combination or Permutation
(and solve)
0011 0010 1010 1101 0001 0100 1011

• We are at the singles, tennis championship.
There are 5 players, Ryan, Megan , Nicole,

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Justin, and Kyle. Each player must play
each other once. How many matches will

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be held?
Combination or Permutation
(and solve)
0011 0010 1010 1101 0001 0100 1011

• How many ways different numbers could
you choose for the Tennessee Pick 5 Lottery

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(generates numbers 1-38)

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