Download Stat 100

Stat 100
Feb. 18
Stat 100
• Read Chapter 15
• Try 1-5, 7, 14, 17, 18, 21, 25
Two Possible Interpretations of
Probability
• Relative Frequency
• Personal Probability
Relative Frequency Interpretation
• Probability is fraction of times an event will
occur over many repeated trials or
observations
• Example: Probability of winning lottery.
Personal Probability
• A subjective or personal number that
reflects the chance of something
• Example: What do you think is the
probability that you’ll graduate within four
years of starting college?
Assignment of Probabilities
• Probabilities might be assigned using:
• physical model
• observation of long run
• personal subjectivity
Probability Values
• Probabilities are numbers between 0 and 1.
• 0= event never occurs
• 1=event always occurs
Opposite Events
• Suppose the chance you you buy a new car
this year is .10. What’s the chance you do
not buy a new car this year?
• Answer=1-.10=.90
• Rule:
Prob of event = 1  Prob of opposite event
Independence and Dependence
• Two events are independent if the chance
one occurs is not affected by whether or not
the other occurs
• Two events are dependent if the chance one
occurs is affected by whether or not the
other occurs
Example
• Are the results of two coin flips independent
or dependent?
• Answer = Independent
• One card is drawn from a 52-card deck.
Then, a second card is drawn. Are the
results independent or dependent?
• Answer = Dependent
Example
• Suppose 20 of 200 women day they like to
gamble.
• And, 45 of 180 men say they like to gamble
• Are liking to gamble and gender
independent or dependent characteristics?
Multiplication Rule
• Multiply probabilities to find the chance
that two or more events occur together or in
a sequence.
Examples
• Chance you correctly guess at two true-false
questions is (1/2)(1/2)=1/4
• What is the chance you correctly guess at 5
True-False Questions?
• Answer = (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32
Example
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Group includes 3 men and 2 women
Two people are picked randomly.
What is the probability both are women?
Answer = (2/5)(1/4) = (2/20) = 1/10
What is the probability that one woman and
one man are picked?
A Spectacular Coincidence ?
• Several states draw four digit lottery
numbers
• Several years ago Mass. and N.H both drew
the same number on the same night
• Associated Press wrote that this was a
spectacular 1 in 100 million coincidence
Was the AP Right ?
• Only if number picked was specified before
draws are made
• Chance both pick the same pre-specified
number is (1/10,000) (1/10,000)
• This is 1 in 100 million
The correct analysis
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First state could picked any number
Prob that second state matches is 1/10,000
Multiplication is 1x(1/10,000)=1/10,000
Even this, may not be right.
The Right Problem
• At the time, 15 states were drawing 4-digit
numbers
• Right problem could be: What’s chance that
2 of 15 states match?
• This has turns out to be about 1 in 100.