Explore IDNLearn.com to discover insightful answers from experts and enthusiasts alike. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.
Sagot :
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
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.
