Transcript P - Cloudfront.net

Section
4.2
Some Probability
Rules—Compound
Events
P(Event A AND Event B)
- Multiply probabilities
- BUT first consider if events are
independent or not
- Ex 1: Roll two fair die.
P(rolling a 5 on both) =
- Ex 2: Six marbles in a bag
(3 green, 2 blue, 1 red)
P(2 green balls w/replacement) =
P(2 green balls w/o replacement) =
2
For ex.1
cont’d
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Conditional Probability
Notation:
P(A|B) means given event B occurred, it’s the probability of
event A occurring
OR
P(B|A) means given event A occurred, it’s the probability of
event B occurring
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Ex 3
P(A= Andrew will be alive in 10 yrs) = 0.72
P(B= Ellen will be alive in 10 yrs) = 0.92
Assuming their lives don’t effect each other…
P(both will be alive in 10 yrs) =
5
Ex 4
100 digital cameras. Drawing 2 at random to check quality
(w/o replacement).
The lot contains 10 defective cameras.
P(both cameras drawn are defective) =
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Multiplication Rule if events are
Independent
Multiplication Rule if events are not
Independent
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Notes:
If two events are independent then,
P(A | B) = P(A)
Or
P(B|A) = P(B)
Ex: P(rolling a 3, given you rolled a 4) =
And you can solve for the conditional probability:
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P(Event A OR Event B)
- Add probabilities
- BUT consider if events are disjoint (or mutually
exclusive)
- Disjoint Events: are events that cannot occur
together. So P(A and B) = 0
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Ex 5
31 students total:
15 freshmen (9 girls, 6 boys)
8 sophomores (3 girls, 5 boys)
6 juniors (4 girls, 2 boys)
2 seniors (1 girl, 1 boy)
a) P(randomly selecting a freshman or sophomore) =
10
cont’d
(b) P(selecting a male or a sophomore) =
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Addition Rule for disjoint events
Addition Rule for non-disjoint
events
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Ex 6
P(slacks being too tight) = 0.30
P(slacks being too loose) = 0.10
a) Are the events mutually exclusive?
b) P(too tight or too loose) =
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Ex 7
Professor is preparing an exam.
P(students need work in math) = 0.80
P(students need work in english) = 0.70
P(need both areas) = 0.55
a) Are the events mutually exclusive?
b) P(need math or need english) =
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Contingency Tables
Employee
Type
Democrat (D) Republican
(R)
Independent
(I)
Row Total
Executive (E) 5
34
9
48
Production
worker (PW)
63
21
8
92
Column total
68
55
17
140 (grant
total)
a)
b)
c)
d)
e)
P(D) =
P(E) =
P(D | E) =
Are D and E independent?
P(D and E) =
P(D or E) =
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Contingency Table continued…
Employee
Type
Democrat (D) Republican
(R)
Independent
(I)
Row Total
Executive (E) 5
34
9
48
Production
worker (PW)
63
21
8
92
Column total
68
55
17
140 (grant
total)
a)
b)
c)
d)
e)
f)
g)
P(I) =
P(PW) =
P(I | PW) =
P(I and PW) =
Use the multiplication rule for P(I and PW) =
Is the answer in c the same as d?
P(I or PW)
Are I and PW mutually exclusive?
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