Probability Explanation And Exercises Worksheet Page 30
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37To define the diagnostic value of the test, we need to define another event:
( 1
) !
=
that you test positive for Disease X. Let's call this Event T. The diagnostic value of
the test depends on the probability you will test positive given that you actually
have the disease, written as P(T|D), and the probability you test positive given that
you do not have the disease, written as P(T|D'). Bayes' theorem shown below
( 1
) !
=
allows you to calculate P(D|T), the probability that you have the disease given that
you test positive for it.
e%Rates%
!
( | ) ( )
!
( | ) =
!
( | ) ( ) + ( | ) ( )
Base%Rates%
The various terms are:
( | ) ( )
( | ) =
!
P(T|D)
= 0.99
( | ) ( ) + ( | ) ( )
P(T|D') = 0.09
P(D)
= 0.02
( 0.99 )( 0.02 )
!
( | ) =
= 0.1833!
P(D')
= 0.98
( 0.99 )( 0.02 ) + ( 0.09 )( 0.98 )
!
Therefore,
( 0.99 )( 0.02 )
( | ) =
= 0.1833!
( 0.99 )( 0.02 ) + ( 0.09 )( 0.98 )
which is the same value computed previously.
%
214
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education