i almost got this one

[rgrocks]

Although highers PSA levels are indicative of cancer, the test is notoriously unreliable. Indeed the probability that a noncancerous man will have an elevated PSA level is approximately .135, with this probability increasing to approximately .268 if the man does have cancer. If, based on other factors a pysician is 70% certain that a male has prostate cancer, what is the conditional probability that he has the cancer given that
a) the test indicated an elevated PSA level
b) the test doesnt indicate an elevated PSA level


First i did was label what they said
E-elevated PSA
NE-not elevated PSA
NC-non cancerious
C-cancerous

P(E|NC)=0.135
P(E|C)=0.268
P(C)=.70

"a" ask us to find P(C|E) but i dont know what P(E) is to use the formula
P(C|E)=[P(E|C)P(C)]/P(E)

"b" find P(C|NE), but i dont know what P(NE|C) is and P(NE)

please help

 

[royhaas]

Construct a 2 by 2 table with joint probabilities. One row should sum to P(cancer) and the other should sum to P(not cancer).
Remember that P(A & B) = P(A|B)P(B) = P(B|A)P(A).