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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

41. An insurance company insured 2000 scooter driver, 4000 car drivers and 6000 truck drivers. The probability of 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?

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alok kumar singh | Contributor-Level 10

4 months ago

41. Let, $E_{1} :$ event that the driver is scooter driver

$E_{2} :$ event that the driver is car driver

$E_{3} :$ event that the driver is truck driver

$A :$ event the person meets with accident

Total number of drivers $= 2000 + 4000 + 6000 = 12000$

$P (E_{1}) = P$ (driver is a scooter driver) $= \frac{2000}{12000} = \frac{1}{6}$

$P (E_{2}) = P$ (driver is a car driver) $= \frac{4000}{12000} = \frac{1}{3}$

$P (E_{3}) = P$ (driver is a truck driver) $= \frac{6000}{12000} = \frac{1}{2}$

$P (A / E_{1}) = P$ (scooter driver met with an accident) $= 0.01 = \frac{1}{100}$

$P (A / E_{2}) = P$ (car driver met with an accident) $= 0.03 = \frac{3}{100}$

$P (A / E_{3}) = P$ (truck driver met with an accident) $= 0.15 = \frac{15}{100}$

The probability that the driver is scooter driver, given that he met with an accident is given by $P (E_{1} / A)$

By Baye’s theorem,

$P (E_{1} / A) = \frac{P (E_{1}) . P (A / E_{1})}{P (E_{1}) . P (A / E_{1}) + P (E_{2}) . P (A / E_{2}) + P (E_{3}) . P (A / E_{3})}$

$= \frac{\frac{1}{6} \times \frac{1}{100}}{\frac{1}{6} \times \frac{1}{100} + \frac{1}{3} \times \frac{3}{100} + \frac{1}{2} \times \frac{15}{100}}$

$= \frac{\frac{1}{600}}{\frac{1}{100} (\frac{1}{6} + 1 + \frac{15}{2})}$

$= \frac{\frac{1}{600}}{\frac{1}{100} (\frac{1 + 6 + 45}{6})}$

$= \frac{\frac{1}{600}}{\frac{1}{100} \times \frac{52}{6}}$

$= \frac{1}{600} \times \frac{600}{52} = \frac{1}{52}$

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41. An insurance company insured 2000 scooter driver, 4000 car drivers and 6000 truck drivers. The probability of 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?

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