STAT 400
Examples for 02/14/2011
Spring 2011
4.
Suppose that on Halloween 6 children come to a house to get treats.
A bag
contains 8 plain chocolate bars and 7 nut bars.
Each child reaches into the bag
and randomly selects 1 candy bar.
Let X denote the number of nut bars selected.
a)
Is the Binomial model appropriate for this problem?
b)
Find the probability that exactly 2 nut bars were selected.
Hypergeometric Distribution
:
N
= population size,
S
= number of “successes” in the population,
N
–
S
= number of “failures” in the population,
n
= sample size.
X
= number of "successes" in the sample when sampling is done without replacement.
Then
n
x
n
x
N
S
N
S
X
C
C
C
N
S
N
S
n
x
n
x
x


⋅
=


⋅
=
=
)
(
P
OR
( )
( )
+

+









+

+



=
=
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
1
1
1
1
1
1
1
1
P
n
x
n
x
x
x
x
x
n
x
N
S
N
...
N
S
N
N
S
N
N
S
...
N
S
N
S
X
max(0,
n
+
S
–
N
)
≤
x
≤
min(
n
,
S
).
EXCEL:
=
HYPGEOMDIST(
x
,
n
,
S
,
N
)
gives
P(X =
x
)
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View Full Document5.
A jar has
N
marbles,
S
of them are orange and
N
–
S
are blue.
Suppose 3 marbles
are selected.
Find the probability that there are 2 orange marbles in the sample, if
the selection is done …
with replacement
without replacement
a)
N
= 10,
S
= 4;
b)
N
= 100,
S
= 40;
c)
N
= 1,000,
S
= 400;
Binomial
Hypergeometric
with replacement
without replacement
Probability
( )
x
n
x
)
X
p
p
x
n
x


⋅
⋅
=
=
1
P(

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 Spring '08
 Kim
 Probability, Binomial distribution, Cumulative distribution function

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