Compound Events

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Compound Events

• A compound event is any event combining two or
  more simple events
• For example, the event exactly 2 girls out of 3
  kids that we considered yesterday.

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1
2
3
4
1
2
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If we put these in a hat and pull one out at
random, what is P(green square) P(numbered
1) P(NOT numbered 1) P(green OR numbered
1) P(green AND numbered 1) P(numbered
1 GIVEN green) P(green GIVEN numbered 1)

3
 If you choose an MM at random, what is   P(is
Blue) P(came from Bag 3) P(NOT Blue)
P(Yellow AND from Bag 2) P(Green OR from Bag
4) P(Orange GIVEN from Bag 3) P(from Bag 3
GIVEN Orange)
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Flip three coins. Find P(none are heads)
P(at least 1 is heads)   Flip two coins.
Find P(first is heads AND second is heads)
P(first is heads OR second is heads) P(second
is heads GIVEN first is heads)
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Write the letters A through J on pieces of paper,
and well pull two out of a hat (without
replacement). Find P(first is B AND second is
G) P(first is B OR first is G) P(second is
A GIVEN first was B) P(second is A GIVEN first
was A)
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Formal Addition Rule(OR statements)

• Addition Rule
• P(A or B) P(A) P(B) P(A and B)
•  
• Idea We want to include the possibilities where
  A happened, and possibilities where B happened,
  but we only want to count each outcomes once.
•  
• Disjoint Events A and B are disjoint if they
  cannot both occur together. In that case, P(A or
  B) P(A) P(B)
•  
• Example P(have 2 kids OR have 3 kids)
• cant have both (at the same time at least)

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Complements

• P(A) P( ) 1 (somethings got to happen)
• So
• P( ) 1 - P(A)
• P(A) 1 - P( )

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Formal Multiplication Rule(AND statements)

• Multiplication Rule
• P(A and B) P(A).P(BA) P(A).P(B given A)
•  
• Idea The probability of A and B happening is
  the probability of A times the probability of B,
  taking into account that A already happened

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Independent Events

• Independent events If the occurrence of one
  does not effect the likelihood of the other
  occurring. Otherwise, the events are dependent.
•  
• Example A number of cups of coffee I drink
  today, B tomorrows weather
•  
• For independent events, P(A and B) P(A) .P(B)
•  
• If were sampling from a large population, if the
  sample is less than 5 of the population, we
  treat the samples as independent (even if we
  sample without replacement and theyre really not
  independent)

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Conditional Probability(GIVEN statements)

• P(BA) P(B given A) P(A and B) / P(A)
•  
• Idea Assume A has happened, and find the
  probability of B occurring

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Homework

• 3.3 1, 3, 5, 9, 11
• 3.4 1, 3, 4, 9, 21
• 3.5 1, 3, 5, 7, 11, 13, 19, 20, 21