Page 116 - Applied statistics and probability for engineers

94 Chapter 3/Discrete Random Variables and Probability Distributions

⎛ 50⎞ ⎛ 800⎞
⎜ ⎝ 0 ⎠ ⎝ 2 ⎠ ⎟
⎟ ⎜
,
(
P X = 0) = = 319 600 = .
0 886
⎛ 850⎞ 360 825
,
⎜ ⎝ 2 ⎠ ⎟
⎛ 50⎞ ⎛ 800⎞
⎟ ⎜
⎜ ⎝ 1 ⎠ ⎝ 1 ⎠ ⎟
,
X (
P X = 1) = = 40 000 = .
0 111
⎛ 850⎞ 360 825
,
⎜ ⎝ 2 ⎠ ⎟
⎛ 50⎞ ⎛ 800⎞
⎟ ⎜
⎜ ⎝ 2 ⎠ ⎝ 0 ⎠ ⎟
(
,
P X = 2) = = 1225 = .
=
0 003
⎛ 850⎞ 360 825
,
⎜ ⎝ 2 ⎠ ⎟
0.8
0.7 N n K
10 5 5
50 5 25
0.6
50 5 3
0.5
0.4
f (x)
0.3
0.2
FIGURE 3-12
Hypergeometric 0.1
distributions for
selected values of 0.0
parameters N, K, 0 1 2 3 4 5
and n. x

Example 3-27 Parts from Suppliers A batch of parts contains 100 from a local supplier of tubing and 200 from a
supplier of tubing in the next state. If four parts are selected randomly and without replacement, what
is the probability they are all from the local supplier?
Let X equal the number of parts in the sample from the local supplier. Then X has a hypergeometric distribution and
(
the requested probability is P X = 4). Consequently,
⎛ 100⎞ ⎛ 200⎞
⎟ ⎜
⎜ ⎝ 4 ⎠ ⎝ 0 ⎠ ⎟
(
P X = 4) = = .
0 0119
⎛ 300⎞
⎜ ⎝ 4 ⎠ ⎟
What is the probability that two or more parts in the sample are from the local supplier?
⎛100 ⎞ ⎛200 ⎞ ⎛100 ⎞ ⎛200 ⎞ ⎛ 100⎞ ⎛ 200⎞
⎜ ⎝ 2 ⎟ ⎜ ⎟ ⎠ ⎜ ⎝ 3 ⎟ ⎜ ⎟ ⎠ ⎜ ⎝ 4 ⎠ ⎝ 0 ⎠ ⎟
⎟ ⎜
⎠ ⎝ 1
⎠ ⎝ 2
P X ≥ 2 ) = + +
(
⎛300 ⎞ ⎛ 3 300⎞ ⎛ 300⎞
⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ 4 ⎠ ⎝ 4 ⎠ ⎝ 4 ⎠
0 298 0 098 0 0 . 1119 =
= . + . + 0 408
.