probabaility help question plz

[ehsanelahimirza]

hi all

i have a question of probability plz help

In a certain region of country it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.05. If the probability of doctor correctly dignosing a person with cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a person without cancer as having the disease is 0.06,what is the probability that a person is diagnosed as having cancer

plz give me its solution

answer is 0.0960 but i cant solve it plz help

 

[claudiocamera]

Lt´s set up the problem:

P(D) = ??? Wanted value
P(C) = 0.05
P(NC) = 0.95
P(D/C) = 0.78
P(D/NC)=0.06

Applying total probability theorem:

P(D) =P(D/C)*P(C) + P(D/NC)*P(NC)

P(D) = 0.78*0.05 + 0.06*0.95 = 0.096

Good luck