Chapter 6 Review

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Chapter 6 Review

• Fr Chris Thiel
• 13 Dec 2004

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What is true about probability?

• The probability of any event must be a number
  between 0 and 1 inclusive
• The sum of all the probabilities of all outcomes
  in the sample space must be 1
• The probability of an event is the sum of the
  outcomes in the sample space which make up the
  event

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Independent
Previous outcomes do not change probability
Multiplication Rule P(A and B)P(A)P(B)
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Disjoint
One outcome precludes the other since there is No
overlap
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Complement
The event A does not occur
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Addition Rules
P(A or B)P(A)P(B)-P(A and B)
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Multiplication Rules
P(A and B)P(A)P(B) if A and B are independent
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Conditional Rules
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P(65)18P(Widowed)10

• If among 65, 44 widowed, What percent of the
  population are widows over 65?

b. If 8 are widows over 65, What is the chance
of being a widow given that theyre over 65?
See Table 6.1 p. 366
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Use Venn Diagrams Trees
Venn Diagrams can help see if events are
Independent, complementary or disjoint
Use Tree Diagrams to Organize addition
and Multiplication rules to combinations of events
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If event A and B are disjoint, then

• P(A and B) 0
• P(A or B) 1
• P(B)1-P(A)

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Independent events you flip a coin and its
heads 4 times in a row. The odds are STILL the
same
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The 6 is 3 times more likely to occur what is
the probability of rolling a 1 or a 6?
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A fair die is tossed4 or 5-win 16-win 4

• If you play twice
• what is the probability that you will win 8?
• 2?

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P(A).5P(B).6P(A andB).1

• P(AB)?
• Are A and B Independent?
• Disjoint?
• Will either A or B always occur?
• Are A and B complementary?

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Lie Detector

• Reports Lie 10 if person is telling the truth
• Reports Lie 95 if the person is actually lying
• Probability of machine never reporting a lie if 5
  truth tellers use it

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You enter a lottery, the odds of getting a prize
is .11If you try 5 times, what is the
probability that you will win at least once?

• 1-P(never winning)

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8 have a disease. A test detects the disease
96 And falsely indicates the disease 7. If you
test positive, what is the chance you have the
disease?
P(D)
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P(Harvard)40 P(Florida)50 P(both)20 P(none)
? P(F but not H)?
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• 30 of calls result in a airline reservation.
• P(10 calls w/o a reservation)?
• b. P(at least 1 out of 10 calls has a
  reservation)?

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85 fire calls are for medical emergencies Assumin
g independence P(exactly one of two calls is
for a medical emergency)?
P(M)P(F)P(F)P(M)(.85)(.15)(.15)(.85).255
Is it really independent?