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# Probability by gabyion

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• pg 1
```									Random Phenomena
   Outcome is unknown before the event
 Flipping a coin
 Rolling a die
 Taking a sample from a population

   Long term behavior is predictable
 16.67% for 1, 2, 3, 4, 5, or 6
 Sampling Distribution (Chapter 18)

1
Probability
   Subjective (Personal)
   Based on feeling or opinion.
   Empirical
   Based on experience.
   Theoretical (Formal)
   Based on assumptions.

2
Chips Example
   Bag o‟ chips (poker chips).
   Some are red.
   Some are white.
   Some are blue.
   Draw a chip from the bag.
   We don‟t know how many of each of the three
colors are in the bag.
   Assumption: Each chip has equal probability of
being chosen (Same size, same weight, same
texture, etc.)
3
The Deal
   Possible out comes of the draw

 Draw a blue chip win 3 bonus points.
 Draw a red chip win 2 bonus points.

 Draw a white chip lose 3 bonus points.

4
Is this a good deal?
   Subjective (personal) probability
   Based on your beliefs and opinion.
   Empirical probability
 Based on experience.
 Conduct a series of trials.

 Each trial has an outcome (R, W, B).

5
Empirical Probability
   Look at the long run relative frequency of
each of the outcomes after choosing n=50
with replacement.
 Blue
 Red

 White

6
Theoretical Probability
   Look in the bag and see how many
 Blue chips –
 Red chips –

 White chips –

   Assumption
   Each chip has the same probability of being
chosen. Equally likely.

7
Law of Large Numbers
   For repeated independent trials, the long
run relative frequency of an outcome gets
closer and closer to the true probability of
the outcome.
   How does this compare with the “Law of
Averages”?

8
Law of Large Numbers
   Probability is a long term number
   Ex. Flip a coin 5 times and get 5 heads in a
row, is a tail due on next flip?
   Random events do not compensate for
short term behavior
   Over a long sequence of flips, even after a
sequence of many heads in a row,
P(tails after sequence) = 0.5

9
Law of Large Numbers
 Over the long term, P(heads) = 0.5
 Long term - Infinite

10
Probability Rules
 A probability is a number between 0 and
1.
 Something has to happen rule.
   The probability of the set of all possible
outcomes of a trial must be 1.

11
Probability Rules
   Event – a collection of outcomes.
   Win bonus points (Blue or Red chip)
   Complement rule
 The probability an event occurs is 1 minus
the probability that it doesn‟t occur.
 P(A) = 1 – P(AC)

12
Probability Rules
 Disjoint events – no outcomes in
common.
 Addition Rule for disjoint events.
 P(A or B) = P(A) + P(B)
 P(Blue or Red) = P(Blue) + P(Red)

13
Probability Rules
   Independent outcomes - The outcome of one
trial does not influence the outcome of the
other.
   1) Coin flips as „Head‟ and 2) Coin flips as
   INDEPENDENT: The outcome of flipping a coin does
not depend on the previous coin flip outcome.
   1) It snows or not and 2) Class is cancelled or
not
   NOT INDEPENDENT: The outcome of 2) depends
on the outcome of 1).
14
Probability Rules
 Independent trials
 Multiplication rule for independent trials.
P(1st outcome and 2nd outcome) =
P(1stoutcome)*P(2nd outcome)

15
Example
   What is the chance that two people in a
row win bonus points?
P(win 1st and win 2nd)=P(win 1st)*P(win 2nd)
P(win 1st) = P(Blue or Red) = P(Blue)+P(Red)
P(win 2st) = P(Blue or Red) = P(Blue)+P(Red)

16
Three Terms to Look For.
   Not
   This means the compliment that is subtract
form 1.
   Or
   This means to add the probabilities.
   And
   This means to multiply the probabilities.

17

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