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(Lesson 11: Multiplication Rule; 44)
4.17
PART C: DEPENDENT EVENTS
P B
A
( )
= the “updated” probability that
B
occurs, given that
A
occurs.
General Multiplication Rule
For events
A
,
B
,
C
, etc.,
P A
and
B
( )
=
P A
( )
⋅
P B
A
( )
P A
and
B
and
C
( )
=
P A
( )
⋅
P B
A
( )
⋅
P C
A
and
B
( )
, etc.
Note: If
A
and
B
are independent, then the occurrence of
A
does not change
our probability assessment for
B
, and
P B
A
( )
=
P B
( )
. In that case, the
General Multiplication Rule becomes the Multiplication Rule for
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Unformatted text preview: Independent Events that we discussed earlier: P A and B ( ) = P A ( ) ⋅ P B ( ) . Example 3 Draw three cards from a standard deck without replacement. (“Without replacement” means that drawn cards are never returned back to the deck.) Find the probability that we draw an Ace first, a King second, and a King third. Think: AKK sequence....
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This note was uploaded on 12/29/2011 for the course MATH 119 taught by Professor Kim during the Fall '09 term at SUNY Stony Brook.
 Fall '09
 KIM
 Multiplication, Probability

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