AP STATISTICS LESSON 6.3 (DAY 1)

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AP STATISTICSLESSON 6.3(DAY 1)

• GENERAL PROBABILITY RULES

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Warm up 1

• Page 323 5.87

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ESSENTIAL QUESTION What are general
probability rules and how are they used to solve
probability problems?

• Objectives
• To become familiar with general probability
  rules.
• To use the general probability rules to solve
  problems.
• To use Venn diagrams, Tree diagrams and tables to
  solve probability problems.

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Rules of probability

• Rule 1 0 P(A) 1 for any A.
• Rule 2 P(S) 1
• Rule 3 Compliment rule For any event A,
• P(Ac) 1 P(A)
• Rule 4 Addition rule If A and B are
  disjoint events, then
• P(A or B ) P(A) P(B)
• Rule 5 Multiplication rule If A and B are
  independent events, then
• P(A and B) P(A)P(B)

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Union

• The union of any collection of events is the
  event that at least one of the collection occurs.

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S

B
A
C
The addition rule for disjoint events P(A or B
or C ) P(A) P( B) P(C) when events A, B,
and C are disjoint.
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Addition rule for disjoint events

• If events A, B, and C are disjoint in the sense
  that no two have any outcomes in common, then
• P( one or more of A, B, C ) P(A) P(B) P(C)
• This rule extends to any number of disjoint
  events.

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Example 6.16

• Page 361

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The general addition rule for the union of two
eventsP(A or B) P(A) P(B) P(A and B)
A and B
B
A
P ( A and B ) is called joint probability.
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General addition rule for unions of two events.

• For any two events A and B
• P(A or B) P(A) P(B) P( A and B )
• Equivalently,
• P(A U B ) P(A) P(B) P( A n B )

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Example 6.17

• Page 362

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Conditional Probability

• P(A/B) Conditional probability gives the
  probability of one event under the condition that
  we know another event.

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Example 6.19

• Page 366

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General Multiplication Rule for any Two Events

• The probability that both of two events A and B
  happen together can be found by
• P(A and B ) P(A)P(B/A)
• Here P(B/A) is the conditional probability that B
  occurs given the information that A occurs.
• In words, this rule says that for both of two
  events to occur, first one must occur and then,
  given that the first event has occurred, the
  second must occur.

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Example 6.20

• Page 368

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Definition of conditional probability

• When P(A) gt 0, the conditional probability of B
  given A is
• P(A/B) P( A and B)
• Be sure to keep in mind the distinct roles in
  P(B/A) of the event B whose probability we are
  computing and the event A that represents the
  information we are given.

P (A)
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Example 6.21

• Page 369