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probability

VIEWS: 68 PAGES: 19

									Basic Rules of Probability
             Vocabulary
• experiment
• sample space - the set S of all possible
  outcomes of an experiment
• event – any subset E of the sample
  space S
• probability – success divided by total
• odds – success to failures
             Vocabulary
• mutually exclusive - events that cannot
  occur at the same time
Determine if the following
events mutually exclusive.
 • E is the event of “being a doctor”
   and F is the event of “being a
   women”
 • E is the event of “being single” and F
   is the event of “being married”
 • E is the event of “being a plumber”
   and F is the event of “being a stamp
   collector”
      Formulas

            n (E )
   p (E ) 
            n (S )

o (E )  n (E ) : n (E ')
Probability Rules

    p ( )  0
    p (S )  1

  0  p (E )  1
        Probability Rules
       p (E )  p (E )  1
p (E  F )  p (E )  p (F )  p (E  F )

            p (E  F )  0
                  if E and F are mutually exclusive
Find the probability of each of
the following:
 • a jack and a heart
 • a jack or a heart
 • not a jack of hearts
 • above a jack
 • below a three
Find the probability of each of
the following:
 • both above a jack and below a three
 • either above a jack or below a three


 • not a jack of hearts
 • above a five
 • below a jack
If o(E) = 1:6, then find o (E ) .
Rolling a Pair of Dice
Find the probability that the sum
when a pair of dice is rolled is
 • 8 or 10


 • even and less than 5


 • even or less than 5
Alex is taking two courses, algebra
and U. S. history. Student records
indicate that the probability of
passing algebra is .35, that of failing
U. S. history is .45, and that of
passing at least one of the two
courses is .80. Find the probability
that
 • Alex will pass history
 • Alex will pass both courses
Alex is taking two courses, algebra
and U. S. history. Student records
indicate that the probability of
passing algebra is .35, that of failing
U. S. history is .35, and that of
passing at least one of the two
courses is .80. Find the probability
that
 • Alex will fail both courses
 • Alex will pass exactly one course
        Formulas
(conditional probability)
                  n (A  B )
     p (A | B ) 
                     n (B )

  p (A  B )  p (A | B )  p (B )
In a newspaper poll concerning violence on
television, 600 people were asked, "What
is your opinion of the amount of violence
on prime-time television -- is there too
much violence on television?". Their
responses are summarized in the table
below.
                            Don’t
           Yes      No              Total
                            Know
Men        162      95       23      280
Women      256      45       19      320
Total      418     140       42      600
                             Don’t
                 Yes   No            Total
                             Know
Men              162   95     23     280
Women            256   45     19     320
Total            418   140    42     600

• p(yes)
• p(men)
• p(yes | men)
• p(men | yes)
• p(yes  men)
• p(men  yes)
Cards are dealt from a full deck
of 52. Find the probability of
each of the given events.

•   the first card is a diamond
•   the second card is a spade, given that the
    first card was a diamond
•   the first card is a diamond and the second
    card is a spade
•   draw a tree diagram illustrating this
A personal computer manufacturer
buys 38% of its chips from Japan and
the rest from America. 1.7% of the
Japanese chips are defective, and
1.1% of the American chips are
defective.
•   Find the probability that a chip is defective
    and made in Japan.
•   Find the probability that a chip is defective
    and made in America.
•   Find the probability that a chip is defective.
•   Find the probability that a chip is defect-free.

								
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