Introductory Biostatistics

PrðY¼þÞ¼

379

24 ; 103

¼ 0 : 015

and

PrðY¼
Þ¼

23 ; 724

24 ; 103

¼ 0 : 985

Note that the sum of the probabilities for each variable is unity:

PrðX¼þÞþPrðX¼
Þ¼ 1 : 0

PrðY¼þÞþPrðY¼
Þ¼ 1 : 0

This is an example of theaddition ruleof probabilities for mutually exclusive
events: One of the two eventsðX¼þÞorðX¼
Þis certain to be true for a
person selected randomly from the population.
Further, we can calculate thejoint probabilities. These are the probabilities
for two events—such as having the diseaseandhaving a positive test result—
occurring simultaneously. With two variables,X andY, there are four con-
ditions of outcomes and the associated joint probabilities are

PrðX¼þ;Y¼þÞ¼

154

24 ; 103

¼ 0 : 006

PrðX¼þ;Y¼
Þ¼

362

24 ; 103

¼ 0 : 015

PrðX¼
;Y¼þÞ¼

225

24 ; 103

¼ 0 : 009

and

PrðX¼
;Y¼
Þ¼

23 ; 362

24 ; 103

¼ 0 : 970

The second of the four joint probabilities, 0.015, represents the probability of
a person drawn randomly from the target population having a positive test
result but being healthy (i.e., afalse positive). These joint probabilities and the

112 PROBABILITY AND PROBABILITY MODELS