Class 12 CBSE Applied Maths Probability Exercise 9.5

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.

Class 12 CBSE Applied Maths Probability Exercise 9.5

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Q1. For the Poisson distribution, find (i) P(2), given λ=0.7 (ii) P(3), given λ = 2.

Q2. Suppose a book of 614 pages contains 43 typographical errors. If these errors are randomly distributed throughout the book, what is the probability that 10 pages, selected at random, will be free of errors?

Q3. Experience shows that 1.4% of the telephone calls received are wrong numbers. Determine the probability that among 150 calls received, two are wrong numbers.

Q4. If 2% of the books bound at a certain workshop have defective binding, find the probability that 5 books out of 400 books will have defective binding.

Q5. It is given that 30% defective electric bulbs are manufactured by a company. Using Poisson distribution, find the probability of 100 bulbs will contain no defective bulb. (use e-3=0.05)

Q6. The mortality rate for a certain disease is 0.007. Using Poisson distribution, calculate the probability for 2 deaths in a group of 400 people

Q7. A computer disk manufacturer tests disk quality on random basis before approving it. The approval is based on the number of errors in a test area on each disk and follow Poisson distribution with λ=0.2. What is the percentage of test areas having two or a smaller number of errors?

Q9. The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 400 men, now aged 35 years, what is the approximate probability that 2 men will die within the next 5 years? (Use e-7.2=0.000747).

Q10. Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 1/5. If 6 bombs are dropped, find the probability that (i) exactly two will strike the target (ii) at least 2 will strike the target

Q11. Ten percent of the bolts produced in a certain factory turn out to be defective. Find the probability, using Poisson distribution, that in a sample of 10 bolts chosen at random, (i) exactly 2 (ii) more than 2 bolts will be defective. (Take e-1 = 0.368)

Q13. There are 500 boxes, each containing 1000 ballot papers for election. The chance that a ballot paper is defective is 0.002. Assuming Poisson distribution, find the number of boxes containing atmost two defective ballot papers. (Use e-2=0.1353)

Q14. Assuming that 200 misprints are distributed randomly throughout a book containing 500 pages, find the probability that a given page contains (i) exactly 2 misprints (ii) 2 or more misprints.

Q15. A box contains 200 tickets, each bearing one of the numbers from 1 to 200, 20 tickets are drawn successively with replacement from the box. Find the probability that atmost 4 tickets bear numbers divisible by 20.

Q16. Find the probability that atmost 5 defective fuses will be found in a box of 200 fuses if experience shows that 2 percent of such fuses are defective.

Q17. A manufacturer of screws knows that 4% of his product is defective. If he sells the screws in boxes of 100 and guarantees that not more than 5 screws will be defective, what is the approximate probability that a box will fail to meet the guaranteed quality?

Q18. The standard deviation of a Poisson variate X is √3. Find the probability that X = 2. (Given e-3=0.0498).

Q19. For a Poisson's distribution, 3P(X = 2) = P(X = 4). Find P(X = 3). Take e-6 = 0.00248.

Q20. Mean of a Poisson distribution is 6.25. Find its variance and standard deviation

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Q1. For the Poisson distribution, find

(i) P(2), given λ=0.7

(ii) P(3), given λ = 2.

Q5. It is given that 30% defective electric bulbs are manufactured by a company. Using Poisson distribution, find the probability of 100 bulbs will contain no defective bulb. (use e^-3=0.05)

Q9. The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 400 men, now aged 35 years, what is the approximate probability that 2 men will die within the next 5 years? (Use e^-7.2=0.000747).

Q10. Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 1/5. If 6 bombs are dropped, find the probability that

(i) exactly two will strike the target
(ii) at least 2 will strike the target

Q11. Ten percent of the bolts produced in a certain factory turn out to be defective. Find the probability, using Poisson distribution, that in a sample of 10 bolts chosen at random,
(i) exactly 2 (ii) more than 2 bolts will be defective. (Take e^-1 = 0.368)

Q13. There are 500 boxes, each containing 1000 ballot papers for election. The chance that a ballot paper is defective is 0.002. Assuming Poisson distribution, find the number of boxes containing atmost two defective ballot papers. (Use e^-2=0.1353)

Q14. Assuming that 200 misprints are distributed randomly throughout a book containing 500 pages, find the probability that a given page contains

(i) exactly 2 misprints
(ii) 2 or more misprints.

Q18. The standard deviation of a Poisson variate X is √3. Find the probability that X = 2. (Given e^-3=0.0498).

Q19. For a Poisson's distribution, 3P(X = 2) = P(X = 4). Find P(X = 3). Take e^-6 = 0.00248.