Question

what is the expression for the probability when the disease D is present but the test says its not? P = Event that test is positive, D = Event disease is present

Answer 1

`P(D\ and\ P^c)` or
`P(D\ and\ P')`

Explanation:

Given

P = Test is positive

D = Disease is present

Required

Write an expression when disease is present but test says that the disease is not present

The above statement can be split to two

Disease is Present & Test is not positive

The first statement:

Disease is Present means D

The second statement

Test is not positive means not P

Mathematically;

not P means P' or
`P^c`

So, the required expression is:
`P(D\ and\ P^c)` or
`P(D\ and\ P')`