Download Vocabulary Law of Large Numbers

Part IV –Randomness and Probability
Ch. 14 – From Randomness to Probability
Vocabulary
• Random Phenomenon:
• Outcome:
• Probability:
• Event:
• Independent:
– Flipping a coin:
– Drawing a card without replacement:
Law of Large Numbers
• The Law of Large Numbers says that
• This only works in the long run – there is no
“Law of Averages” telling us what will happen
on any particular trials
Symbols of Probability
• P(A) = the probability that event A will occur
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–
–
• Sample space (S):
– Ex. Flipping a coin three times
Symbols of Probability
• Complement (Ac):
–Ex. A North student is randomly
selected
• A = the student is a senior
• Ac =
Calculating Simple Probabilities
• If all outcomes are equally likely:
– Ex. Flipping a coin 3 times
• P(exactly 2 heads) =
– Ex. Rolling a 6-sided die
• P(5)=
• P(even #)=
• P(7)=
Basic Probability Rules
1)
All probabilities are between 0 and 1
2)
The probability of the sample space (all the
outcomes added together) must be 1, since we
are certain that some outcome will occur
3)
The probability that A occurs is 1 minus the
probability that it doesn’t occur
-ex. P(you’ll get an A in statistics) = .40
P(won’t get an A) =
Vocabulary
• Disjoint or Mutually Exclusive:
– Ex. Drawing a card from a deck
• A = Card is a Jack
B = Card is a 7
• A = Card is a Jack
B = Card is a spade
Two more rules…
4) Addition Rule: If A and B are disjoint,
- Ex. Draw one card from a deck
P(Jack or Queen) =
5) Multiplication Rule: If A and B are
independent, then
- Ex. Roll a die twice
P(6 and then a 5) =
Things to Remember
• The last two rules only work under certain
conditions – make sure you first verify that
these conditions are met!
• Don’t mix these up:
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Let’s Practice…
Opinion polling organizations contact their respondents
by telephone. Random telephone numbers are
generated and interviewers try to contact those
households. In the 1990s this method could reach
about 69% of U.S. households. According to the Pew
Research Center for the People and the Press, by 2003
the contact rate had risen to 76%.
a) What is the probability that the interviewer will successfully
contact the next household on the list?
b) What is the probability that an interviewer successfully
contacts both of the next two households on her list?
c) What is the probability that the interviewer’s first successful
contact will be the third household on the list?
Using the Complement – “At least one”
d) What is the probability that the interviewer
will make at least one successful contact
among the next 5 households on the list?
When a problem says “at least one”, it is usually
easiest to use the complement rule:
Homework
• p. 339-343
#9 – 33 odd
• These are odd problems – check your answers!
• Refer to the rules as you work – remember
that for a probability distribution to be
legitimate:
– the sum of the probabilities of all outcomes has to
equal one
– all probabilities have to be between 0 and 1