Math 120 SP08 SBrodnick
1
1
7.6
Applications
2
* A red dish and a green dish both contain blue
and white poker chips.
The probability of
choosing the red dish is 0.40, and the
probability of drawing a blue chip from the red
dish is 0.70, whereas the probability of drawing
a blue chip from the green dish is 0.60.
Set up a probability tree to find
a. P(B’R)
b. P(G
∩
B)
c. P(B)
d. P(GB)
3
*
Bayes’ Theorem
(for
two
possibilities at each branch)
P(AT) =
* You need Bayes’ Theorem when the “
given that
”
event
happens later
on the tree, and you need
to work
backwards
A
A'
T
T'
T
T'
P(TA) · P(A)
P(TA) · P(A) + P(TA') · P(A')
4
Examples
:
1. Given the following tree, compute P(BC).
2.For two events M and N,
P(M) = 0.6,
P(NM) = 0.5, and
P(NM') = 0.2.
Use Bayes’ Theorem to find
a. P(MN)
b. P(M'N)
B
B'
C
C'
0.2
0.7
C
C'
0.9
0.8
0.3
0.1
5
3.For a fixed length of time, the probability of
worker error on a certain production line is
0.06, the probability that an accident will occur
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Brodnick
 Math, Conditional Probability, Probability theory, Bayesian probability, Midwestern United States

Click to edit the document details