Since 31 of those who carry insurance are surgeons, the other 58-31= 27 are not. Since 33 of the 64 medical workers are surgeons, the other 64- 33= 31 are not. This whole group can be divided into 4 separate groups: 31 surgeons who carry insurance, 33- 31= 2 surgeons who do not carry insurance, 27 non-surgeons who carry insurance, and 31- 27= 4 non-surgeons who do not carry insurance.

Assuming that random here means all medical workers are "equally likely" to be chosen, this the number of surgeon who do not carry insurance divided by the total number of medical workers, 2/64.a. If one of these medical workers is randomly chosen what is the probability that he is not a surgeon and does not carry insurance.

This is the number of non-surgeons that carry insurance divided by the number of non-surgeons, 27/31.b. Find the probability that he carries insurance given that he is not a surgeon.