I'm new to statistics and have a simple probability problem:

The probabilities associated with the expected principal source of payment for hospital discharges in the United States in the year 1990 are listed below:

Principal Source of Payment Probability

Private Insurance 0.387
Medicare 0.345
Medicaid 0.116
Other govt. program 0.033
Self-payment 0.058
Other/No charge 0.028
Not stated 0.033

total: 1.000

a). What is the probability that the principal source of payment for a given hospital discharge is the patient’s private insurance (0.387)?
b). What is the probability that the principal source of payment is medicare (0.345), medicaid (0.116) or some other govt. program (0.033)?
c). Given that the probability source of payment is a government program what is the probability that it is Medicare (0.345)?

b): They what to know the probability of medicare, medicaid, or some other gov;t program, not each probability individually. Add them up.

c): What is the probability that it's Medicare given they pay with a gov't program. What's the total proabilities of the gov't programs? Medicaid, medicare, other.

You know, what you could do is make a chart with assumed numbers. Say, a total of 1000 participants.