Question

Condition Condition Present Absent Row Total Test Result + 110 130 Test Result - 20 50 70 Column Total 130 200 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities: (a) P(+ condition present); this is known as the sensitivity of a test. (b) PC- I condition present); this is known as the false-negative rate. (c) P(- I condition absent); this is known as the specificity of a test. (d) P(+ I condition absent); this is known as the false-positive rate. (e) P(condition present and + ); this is the predictive value of the test. (f) P(condition present and - ). 211

Answer 1

Answer:

Given table,

	Condition Present	Condition Absent	Row Total
Test Result +	110	20	130
Test Result -	20	50	70
Column Total	130	70	200

(a).

P( + | Condition Present):

P( + | Condition Present)=( + $\cap$ Condition Present)/P(Condition Present)

=(110/200)/(130/200)

=0.55/0.65

=0.8462

(b).

P( - | Condition Present):

P( - | Condition Present)=( - $\cap$ Condition Present)/P(Condition Present)

=(20/200)/(130/200)

=(0.1)/(0.65)

=0.1538

(c).

P( - | Condition Absent):

P( - | Condition Absent)=( - $\cap$ Condition Absent)/P(Condition Present)

=(50/200)/(70/200)

=(0.25)/(0.35)

=0.7143

(d).

P( + | Condition Absent):

P( + | Condition Absent)=( + $\cap$ Condition Absent)/P(Condition Absent)

=(20/200)/(70/200)

=(0.1)/(0.35)

=0.2857

(e).

P(Condition present and +):

P(Condition present and +)=P(Condition Present $\cap$ +)

=P(+ $\cap$ Condition Present)

=110/200

=0.55

(f).

P(Condition present and -):

P(Condition present and -)=20/200

=0.1