Probablity question

Question

At a hospital, in a sample group,  there are 40 patients who have lung cancer and 30 patients who are smokers.  Of these, 25 smoke and have lung cancer.  If the hospital currently has 200 patients and one is chosen at random for a medical study, what is the probability the patient has lung cancer, given that the patient smokes?   Please show work and give an explanation.

Answer 1

We want P(lung cancer|smokes)

P(lung cancer|smokes)

= P(lung cancer and smokes) / P(smokes)

= (25/40) / (30/40)

= 5/6

Answer 2

Hi Dana from my hometown,

 

30/200 are smokers in the hospital, 15%. You may be able to ignore this though.  If you select a smoker, then 25/30 smokers have lung cancer, 83.3% chance that a smoker chosen will have have lung cancer.

If you truly selected at random from the 200, the odds that one of them is a smoker with cancer is 25/200, or 12.5%

 

Maybe someone else will comment too.

 

Regards,

Jim Gibbs, Sugar Land, TX

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Jim Gibbs

Answer 3

 A - people who have long Cancer = 40

 

  B - 30 who are smoker

 

  A ^ B =  Patients who have long cancer and smoker= 25

 

   people who have long cancer = (A + B)  -  B - A^B = 70 - 30 - 25 = 15

 

  P ( A I B ) * P( B)=  30/70 * 25/70 = 15/98