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Sagot :
Answer:
0.2027 = 20.27% probability that the person is a moderate-risk policy holder
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It 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 question:
Event A: Policy holder files a claim.
Event B: The person is a moderate-risk policy holder.
Probability of filling a claim:
5% of 55%(low risk)
15% of 25%(moderate risk)
60% of 20%(high risk).
So
[tex]P(A) = 0.05*0.55 + 0.15*0.25 + 0.6*0.2 = 0.185[/tex]
Files a claim and is moderate risk:
15% of 25%(moderate risk)
So
[tex]P(A \cap B) = 0.15*0.25 = 0.0375[/tex]
Given that a policy holder files a claim this year, what is the probability that the person is a moderate-risk policy holder?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0375}{0.185} = 0.2027[/tex]
0.2027 = 20.27% probability that the person is a moderate-risk policy holder
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