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An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?
- a)3/52
- b)5/52
- c)1/52
- d)1/4
Correct answer is option 'C'. Can you explain this answer?
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An insurance company insured 2000 scooter drivers, 4000 car drivers an...
Let
E1 , E2 and E3 and are events of selection of a scooter driver , car driver and truck driver respectively.
E1 , E2 and E3 and are events of selection of a scooter driver , car driver and truck driver respectively.
Most Upvoted Answer
An insurance company insured 2000 scooter drivers, 4000 car drivers an...
To solve this problem, we can use Bayes' theorem, which is a fundamental concept in probability theory. Bayes' theorem allows us to update our probability estimates based on new information.
Let's define the events:
S = The insured person is a scooter driver
C = The insured person is a car driver
T = The insured person is a truck driver
A = The insured person meets with an accident
We are given the following probabilities:
P(S) = 2000/12000 = 1/6 (There are 2000 scooter drivers out of a total of 12000 drivers)
P(C) = 4000/12000 = 1/3 (There are 4000 car drivers out of a total of 12000 drivers)
P(T) = 6000/12000 = 1/2 (There are 6000 truck drivers out of a total of 12000 drivers)
P(A|S) = 0.01 (The probability of an accident given that the person is a scooter driver)
P(A|C) = 0.03 (The probability of an accident given that the person is a car driver)
P(A|T) = 0.15 (The probability of an accident given that the person is a truck driver)
We are asked to find the probability that the person is a scooter driver given that they have met with an accident, i.e. P(S|A).
We can use Bayes' theorem to calculate this probability:
P(S|A) = (P(A|S) * P(S)) / P(A)
Calculating P(A):
P(A) = P(A|S) * P(S) + P(A|C) * P(C) + P(A|T) * P(T)
= (0.01 * 1/6) + (0.03 * 1/3) + (0.15 * 1/2)
= 1/600 + 1/100 + 3/20
= (1 + 6 + 90) / 600
= 97/600
Now substituting the values in the equation for P(S|A):
P(S|A) = (0.01 * 1/6) / (97/600)
= (1/600) / (97/600)
= 1/97
Therefore, the probability that the insured person is a scooter driver given that they have met with an accident is 1/97, which is equivalent to option C) 1/52.
Let's define the events:
S = The insured person is a scooter driver
C = The insured person is a car driver
T = The insured person is a truck driver
A = The insured person meets with an accident
We are given the following probabilities:
P(S) = 2000/12000 = 1/6 (There are 2000 scooter drivers out of a total of 12000 drivers)
P(C) = 4000/12000 = 1/3 (There are 4000 car drivers out of a total of 12000 drivers)
P(T) = 6000/12000 = 1/2 (There are 6000 truck drivers out of a total of 12000 drivers)
P(A|S) = 0.01 (The probability of an accident given that the person is a scooter driver)
P(A|C) = 0.03 (The probability of an accident given that the person is a car driver)
P(A|T) = 0.15 (The probability of an accident given that the person is a truck driver)
We are asked to find the probability that the person is a scooter driver given that they have met with an accident, i.e. P(S|A).
We can use Bayes' theorem to calculate this probability:
P(S|A) = (P(A|S) * P(S)) / P(A)
Calculating P(A):
P(A) = P(A|S) * P(S) + P(A|C) * P(C) + P(A|T) * P(T)
= (0.01 * 1/6) + (0.03 * 1/3) + (0.15 * 1/2)
= 1/600 + 1/100 + 3/20
= (1 + 6 + 90) / 600
= 97/600
Now substituting the values in the equation for P(S|A):
P(S|A) = (0.01 * 1/6) / (97/600)
= (1/600) / (97/600)
= 1/97
Therefore, the probability that the insured person is a scooter driver given that they have met with an accident is 1/97, which is equivalent to option C) 1/52.
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An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?a)3/52b)5/52c)1/52d)1/4Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?a)3/52b)5/52c)1/52d)1/4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?a)3/52b)5/52c)1/52d)1/4Correct answer is option 'C'. Can you explain this answer?.
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