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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
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