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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?

Respuesta :

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:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] 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 [tex]P(A) = 0.35[/tex].
  • Of those who have Medicare, there is a 10% chance they also have Medicaid, hence [tex]P(B|A) = 0.1[/tex].

Then, applying the conditional probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]0.1 = \frac{P(A \cap B)}{0.35}[/tex]

[tex]P(A \cap B) = 0.35(0.1)[/tex]

[tex]P(A \cap B) = 0.035[/tex]

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

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

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