Define sample space'

1

• Define sample space.
• Give the sample space for the sum of the numbers
  for a pair of dice.
• You flip four coins. Whats the probability of
  getting exactly two heads? (Hint List the
  outcomes first).
• Joey is interested in investigating so-called hot
  streaks in foul shooting among basketball
  players. Hes a fan of Carla, who has been making
  approximately 80 of her free throws.
  Specifically, Joey wants to use simulation
  methods to determine Carlas longest run of
  baskets on average, for 20 consecutive free
  throws.
• a) Describe a correspondence between random
  digits from a random digit table and outcomes.
• b) What will constitute one repetition in this
  simulation?
• c) Starting with line 101 in the random digit
  table, carry out 4 repetitions and record the
  longest run for each repetition.
• d) What is the mean run length for the 4
  repetitions?

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6.2 Notes (2nd ½)
3
Disjoint/Complement
4
Ex. 6.13, p. 419

• Find the probability that the student is not in
  the traditional undergraduate age group of 18-23
• Find P(30 years)

5
Venn Diagram

• Find P(A), P(B), P(C)
• Find P(A), P(B), P(C)

6
Example

• If the chances of success for surgery A are 85
  and the chances of success for surgery B are 90,
  what are the chances that both will fail?

7
Venn Diagram Union (Or/Addition Rule)

• Find
• P(AUB) getting an even number or a number
  greater than or equal to 5 or both
• P(AUC) getting an even number or a number less
  than or equal to 3 or both
• P(BUC)getting a number that is at most 3 or at
  least 5 or both.

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Ex. 6.14, p. 420

• Because all 36 outcomes together must have
  probability 1 (Rule 2), each outcome must have
  probability 1/36.

• CLASS Now find P(rolling a 7)

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Ex. 6.15, p. 421

• Consider the events A first digit is 1, B
  first digit is 6 or greater, and C a first
  digit is odd
• Find P(A) and P(B)
• Find P(complement of A)
• Find P(A or B)
• Find P(C)
• Find P(B or C)

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Ex. 6.16, p. 422

• Find the probability of the event B that a
  randomly chosen first digit is 6 or greater.

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• The probability that BOTH events A and B occur
• A and B are the overlapping area common to both A
  and B
• Only for INDEPENDENT events

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Venn Diagram Intersection (And/ Rule)

• Find
• P(A and B) getting an even number that is at
  least 5
• P(A and C) getting an even number that is at
  most 3
• P(B and C)getting a number that is at most 3 and
  at least 5.

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Finding the probability of at least oneP(at
least one) 1-P(none)

• Many people who come to clinics to be tested for
  HIV dont come back to learn the test results.
  Clinics now use rapid HIV tests that give a
  result in a few minutes. Applied to people who
  dont have HIV, one rapid test has probability
  about .004 of producing a false-positive. If a
  clinic tests 200 people who are free of HIV
  antibodies, what is the probability that at least
  one false positive will occur?
• N 200
• P(positive result) .004, so P(negative
  result)1-.004.996

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Big Picture

• Rule holds if A and B are disjoint/mutually
  exclusive
• Rule holds if A and B are independent
• Disjoint events cannot be independent! Mutual
  exclusivity implies that if event A happens,
  event B CANNOT happen.

15
Conditional probability Pre-set condition
(given)

• Find
• P(A given C) getting an even number GIVEN that
  the number is at most 3.
• P(A given B) getting an even number GIVEN that
  the number is at least 5.

16

• In building new homes, a contractor finds that
  the probability of a home-buyer selecting a
  two-car garage is 0.70 and selecting a one-car
  garage is 0.20. (Note that the builder will not
  build a three-car or a larger garage).
• What is the probability that the buyer will
  select either a one-car or a two-car garage?
• Find the probability that the buyer will select
  no garage.
• Find the probability that the buyer will not want
  a two-car garage.