Introductory Statistics
Probability
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Heads or Tails
Parents Getting a Girl
Blood Type
Getting Brown Eyes
Rolling a Seven in a game of monopoly
Probability of Getting Rained Upon in a Picnic
Winning in Roulette
Winning a Million Dollars in the Lottery
Rare or Unusual Events (Term to Know in Inferential Statistics)
Three Probability Rules
The probability of any event must be greater than
or equal to 0 –and- less than or equal to 1.
• Sum of all Probabilities of all possible outcomes
must equal 1.
• If E represents an event, P(E) is the probability of
that event, then the probability of that event not
happening is 1-P(E) – Complement Rule.
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Three Probability Rules
The probability of any event must be greater than or
equal to 0 –and- less than or equal to 1.
Sum of all Probabilities of all possible outcomes must
equal 1.
If E represents an event, P(E) is the probability of that
event, then the probability of that event not happening
is 1-P(E) – Complement Rule.
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Example One
Number of Heads from Two Flips
Event
0
1
Probability
0.25
0.5
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2
0.15
True Probability Model? No – Second Rule Doesn’t apply
Example Two
Number of Heads from Two Flips
Event
0
1
Probability
0.25
0.5
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2
0.25
True Probability Model? Yes – First two rules apply
Probability of only getting one head in two flips? 50%
Probability of not getting one head in two flips (0 or 2 heads)? 1-50%=50%
HH
HT
TH
TT
Three Probability Rules –Page 2
Example Three – Empirical Data
Event
Probability
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Red
Green
0.1
M&M's in a Bag
Blue
Brown
0.1
0.1 ?
Yellow
Orange
0.2
0.3
What is the probability of drawing a brown M&M? 0.2
What is the probability of not drawing a brown M&M? 0.8
What is the probability of not drawing a yellow M&M? 0.8
Example Four – # of girls with three children (assuming the same likelihood for boy/girl)
Number of Girls
0
1
2
3
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Probability
1/8
3/8
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1/8
What is the probability of getting exactly two girls? 3/8
What is the probability of not getting exactly two girls? 5/8
What is the probability of getting no more than one girl? 4/8 = 1/2
Mean and Variance of Discrete Random Variable
Number of Heads from Two Flips
Event (Xi)
0
1
2
Probability (Pi)
0.25
0.50
0.25
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Mean of Discrete Random Variable
Mean = (0 * 0.25) + (1 *0.50) + (2 *.25) = 0 + 0.5 +0.5 = 1
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Variance of Discrete Random Variable
Variance = [(0-1)2 * 0.25] + [(1-1)2 * 0.5] + [(2-1)2 * 0.25] = .25 + 0 + .25 = .5
Standard Deviation = . 𝟓= .707
Use excel to compute Mean, Variance and Standard Deviation of
Discrete Random Variable