Dependent and Independent Events (solns).notebook
Dependent &
Independent
Events
(some possible
solutions)
Dep & Indep Events
November 19, 2009
Dependent and Independent Events (solns).notebook
1
November 19, 2009
Dependent and Independent Events (solns).notebook
2 direct
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Dependent and Independent Events (solns).notebook
= 1 ­ 2b) indirect
November 19, 2009
Dependent and Independent Events (solns).notebook
3
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Dependent and Independent Events (solns).notebook
4
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Dependent and Independent Events (solns).notebook
5
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Dependent and Independent Events (solns).notebook
6b
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Dependent and Independent Events (solns).notebook
some dice
November 19, 2009
Dependent and Independent Events (solns).notebook
9
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Dependent and Independent Events (solns).notebook
9
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Dependent and Independent Events (solns).notebook
10 version 1
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Dependent and Independent Events (solns).notebook
10 version 2
November 19, 2009
Dependent and Independent Events (solns).notebook
November 19, 2009
tree
box Venn
P
P
D
D
12 (models)
Dependent and Independent Events (solns).notebook
November 19, 2009
tree
box Venn
P
P
D
D
check sums = 1
12 (given)
Dependent and Independent Events (solns).notebook
12 solns
November 19, 2009
Dependent and Independent Events (solns).notebook
13
November 19, 2009
Dependent and Independent Events (solns).notebook
November 19, 2009
P(begins with L | ends with A)
P(L _ _ _ _ _ _ A)
P( _ _ _ _ _ _ _ A)
n(L _ _ _ _ _ _ A)
n( _ _ _ _ _ _ _ A)
BASEL
A BASEL
B L answer = (i)
(ii)
14
Dependent and Independent Events (solns).notebook
"this is a terrible solution"
­­ the Shim
15 terrible
November 19, 2009
Dependent and Independent Events (solns).notebook
CHANE
C
CHOIE
C
P(same)
=P(CC) + P(HH) + P(EE)
15 good
November 19, 2009
Dependent and Independent Events (solns).notebook
6R 4G
18c
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Dependent and Independent Events (solns).notebook
19
November 19, 2009
Dependent and Independent Events (solns).notebook
November 19, 2009
DeMorgan's Law
B
A
B
A
deMorgan's Law
Dependent and Independent Events (solns).notebook
November 19, 2009
20. G: is a girl
P(all G | at least 1G)
P(all G ∩ at least 1G)
P(at least 1G)
20
Dependent and Independent Events (solns).notebook
November 19, 2009
21.
D: are defective
H: made by high speed machine
M: made by medium spd machine
L: made by low speed machine
M
H
L
D
21
Dependent and Independent Events (solns).notebook
22.
November 19, 2009
T: are taller than 178 cm
D: completes degree
T & D are indep
a) P(T ∩ D)
b) P(T' ∩ D')
c) P(T ∪ D)
22
Dependent and Independent Events (solns).notebook
November 19, 2009
23. {0, 1, 2, 3, ... , 9}
+
1st digit
=
2nd digit
digit sum
sweet cases!
{0, 7}
{1, 6}
x 2
{2, 5}
{3, 4}
}
P(sum = 7) = 8 cases
100
23
Dependent and Independent Events (solns).notebook
November 19, 2009
24. D: roll doubles
1
P(D)=
6
1
P(DD)=
36
P(DD times)=?
(strategy: simplify the question)
Consider 6 rolls.
or, indirect?
1­P(42D')­P(41D', 1D)
24