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A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________
Correct answer is '0.67'. Can you explain this answer?
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A survey of people in given region showed that 25% drank regularly. Th...
Given:
- 25% of people in a region drink regularly.
- Probability of death due to liver disease, given that a person drinks regularly is 6 times the probability of death due to liver disease, given that a person does not drink regularly.
- Probability of death due to liver disease in the region is 0.005.
To Find:
- Probability that a person who died due to liver disease drank regularly.
Solution:
Let A be the event that a person drinks regularly, and B be the event that a person dies due to liver disease.
We are given P(A) = 0.25, P(B) = 0.005, P(B|A) = 6*P(B|A').
We need to find P(A|B).
Using Bayes' theorem, we have:
P(A|B) = P(B|A)*P(A)/P(B)
We can find P(B) using the law of total probability:
P(B) = P(B|A)*P(A) + P(B|A')*P(A')
Substituting the given values, we get:
P(B) = 6*P(B|A')*0.75 + P(B|A)*0.25
P(B) = 1.5*P(B|A') + 0.25*P(B|A)
Now, we can substitute P(B) and P(B|A) in the equation for P(A|B) to get:
P(A|B) = 6*P(B|A')*P(A)/(1.5*P(B|A') + 0.25*P(B|A))
Substituting the given values, we get:
P(A|B) = 6*0.995*0.25/(1.5*0.995 + 0.25*0.005)
P(A|B) = 0.67
Therefore, the probability that a person who died due to liver disease drank regularly is 0.67.
- 25% of people in a region drink regularly.
- Probability of death due to liver disease, given that a person drinks regularly is 6 times the probability of death due to liver disease, given that a person does not drink regularly.
- Probability of death due to liver disease in the region is 0.005.
To Find:
- Probability that a person who died due to liver disease drank regularly.
Solution:
Let A be the event that a person drinks regularly, and B be the event that a person dies due to liver disease.
We are given P(A) = 0.25, P(B) = 0.005, P(B|A) = 6*P(B|A').
We need to find P(A|B).
Using Bayes' theorem, we have:
P(A|B) = P(B|A)*P(A)/P(B)
We can find P(B) using the law of total probability:
P(B) = P(B|A)*P(A) + P(B|A')*P(A')
Substituting the given values, we get:
P(B) = 6*P(B|A')*0.75 + P(B|A)*0.25
P(B) = 1.5*P(B|A') + 0.25*P(B|A)
Now, we can substitute P(B) and P(B|A) in the equation for P(A|B) to get:
P(A|B) = 6*P(B|A')*P(A)/(1.5*P(B|A') + 0.25*P(B|A))
Substituting the given values, we get:
P(A|B) = 6*0.995*0.25/(1.5*0.995 + 0.25*0.005)
P(A|B) = 0.67
Therefore, the probability that a person who died due to liver disease drank regularly is 0.67.
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Community Answer
A survey of people in given region showed that 25% drank regularly. Th...
Let A = Person drinks regularly
B = Death due to liver disease
P (A) = 0.25 and P (B) = 0.005
= 2/3
= 0.67
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A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer?
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A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer?.
A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer?.
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A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer?, a detailed solution for A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer? has been provided alongside types of A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly was 6 times the probability of death due to liver disease, given that a person did not drink regularly. The probability of death due to liver disease in the region is 0.005. If a person dies due to liver disease, the probability that he/she drank regularly is _____________Correct answer is '0.67'. Can you explain this answer? theory, EduRev gives you an
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