Question

A hospital’s financial reimbursement payor mix indicates 35% of the patients have Medicare and 15% have Medicaid. Of those who have Medicare, there is a 10% chance they also have Medicaid. What is the probability that a hospital patient has both Medicare and Medicaid?

Answer 1

Using conditional probability, it is found that there is a 0.035 = 3.5% probability that a hospital patient has both Medicare and Medicaid.

What is Conditional Probability?

• Conditional probability is the probability of one event happening, considering a previous event. The formula is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

• P(B|A) is the probability of event B happening, given that A happened.

• $P(A \cap B)$ is the probability of both A and B happening.

• P(A) is the probability of A happening.

In this problem, the events are:

• Event A: Patient has Medicare.

• Event B: Patient has Medicaid.

For the probabilities, we have that:

• 35% of the patients have Medicare, hence $P(A) = 0.35$.

• Of those who have Medicare, there is a 10% chance they also have Medicaid, hence $P(B|A) = 0.1$.

Then, applying the conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.1 = \frac{P(A \cap B)}{0.35}$

$P(A \cap B) = 0.35(0.1)$

$P(A \cap B) = 0.035$

0.035 = 3.5% probability that a hospital patient has both Medicare and Medicaid.

You can learn more about conditional probability at brainly.com/question/14398287