CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari

Probability

Q.7. A manufacturing firm produces steel pipes in three plants A, B and C with daily production of 500, 1000 and 2000 units respectively. The fractions of defective steel pipes output produced by the plant A, B and C are respectively 0.005, 0.008 and 0.010. If a pipe is selected from a day’s total production and found to be defective, find out the probability that it came from the first plant.

Solution :

We have probability of production,
P(A) = 500/3500 = 1/7,
P(B) = 1000/3500 = 2/7,
P(C) = 2000/3500 = 4/7.
And probability of defective pipes,
By plant A = P(A/E) = 0.005,
By plant B = P(B/E) = 0.008,
By plant C = P(C/E) = 0.010.
Therefore by Baye’s Theorem, probability of defective pipe from first plant
= P(E/A) = [P(A)×P(A/E)]/[P(A).P(A/E) + P(B).P(B/E) + P(C).P(C/E)]
= [1/7×0.005]/[1/7×0.005 + 2/7×0.008 + 4/7×0.010]
= 0.005/[0.005 + 0.016 + 0.040]
= 0.005/0.061 = 5/61[Ans.]

Q.8. An insurance company insured 6000 scooter drivers, 3000 car drivers and 9000 truck drivers. The probability of an accident involving a scooter, a car and a truck is 0.02, 0.06 and 0.30 respectively. One of the insured persons meets with an accident. Find the probability that he is a car driver.

Solution :

Let A, B and C be the event that the insured person is scooter driver, car driver and truck driver and E be the event when an insured person meets with an accident.
Therefore, the probability P(A) = 6000/(6000 + 3000 + 9000) = 6000/18000 = 1/3,
P(B) = 3000/(6000 + 3000 + 9000) = 3000/18000 = 1/6,
P(C) = 9000/(6000 + 3000 + 9000) = 9000/18000 = 1/2 .
It is given that P(E/A) = 0.02, P(E/B) = 0.06 and P(E/C) = 0.30.
Hence by Baye’s Theorem,
P(B/E) = [P(B)P(E/B)]/[P(A)P(E/A) + P(B)P(E/B) + P(C)P(E/C)
= {1/6(6/100)}/[ {1/3(2/100) + 1/6(6/100) + 1/2(30/100)}
= 1/[(2/3) + 1 + 15] = 3/50 = 0.06.[Ans.]

Q.9. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truck 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.

Solution :

Do yourself. [Ans. = 1/52]

Q.10. An insurance company insured 4000 doctors, 8000 teachers and 12000 engineers. The probabilities of a doctor, a teacher and an engineer dying before the age of 58 years are 0.01, 0.03 and 0.05 respectively. If one of the insured person dies before the age of 58 years, find the probability that he is a doctor.

Solution :

Do yourself. [Ans. = 1/22]

Paper By Mr. M.P.Keshari
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