Using simultaneous equations to find probability of...

Hi all,

I can work the following with a tree diagram but not with simultaneous equations:

75% of patients who have cancer and 10% of normal patients (who do not have cancer) are diagonised with cancer by a MRI. If 15% of a population have cancer, what is the probability of patients who are digonised with cancer by a MRI that really do have cancer?

Using a tree diagram, i get probabilty of patients being diagonised which actually have cancer

= (0.15 * 0.75)/ [(0.15 * 0.75) + (0.85 * 0.1)]

= 0.57

Thanks in advance,

ArTiCk