Page 287 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 2. Define a binomial distribution. State the conditions under which binomial probability
model is appropriate.
3. What are the parameters of a binomial distribution? Obtain expressions for mean and
variance of the binomial variate in terms of these parameters.
4. Assume that the probability that a bomb dropped from an aeroplane will strike a target is
1/5. If six bombs are dropped, find the probability that (i) exactly two will strike the
target, (ii) at least two will strike the target.
5. An unbiased coin is tossed 5 times. Find the probability of getting (i) two heads, (ii) at least
two heads.
6. An experiment succeeds twice as many times as it fails. Find the probability that in 6 trials
there will be (i) no successes, (ii) at least 5 successes, (iii) at the most 5 successes.
7. In an army battalion 60% of the soldiers are known to be married and remaining unmarried.
If p(r) denotes the probability of getting r married soldiers from 5 soldiers, calculate p(0),
p(1), p(2), p(3), p(4) and p(5). If there are 500 rows each consisting of 5 soldiers, approximately
how many rows are expected to contain (i) all married soldiers, (ii) all unmarried soldiers?

8. A company has appointed 10 new secretaries out of which 7 are trained. If a particular
executive is to get three secretaries, selected at random, what is the chance that at least one
of them will be untrained?
9. The overall pass rate in a university examination is 70%. Four candidates take up such
examination. What is the probability that (i) at least one of them will pass (ii) at the most
3 will pass (iii) all of them will pass, the examination?
10. 20% of bolts produced by a machine are defective. Deduce the probability distribution of
the number of defectives in a sample of 5 bolts.
11. 25% employees of a firm are females. If 8 employees are chosen at random, find the
probability that (i) 5 of them are males (ii) more than 4 are males (iii) less than 3 are
females.
12. Suppose that the probability is that a car stolen in Delhi will be recovered. Find the
probability that at least one out of 20 cars stolen in the city on a particular day will be
recovered.
13. A sales man makes a sale on the average to 40 percent of the customer he contacts.
If 4 customers are contacted today, what is the probability that he makes sales to exactly
two? What assumption is required for your answer?

14. In a binomial distribution consisting of 5 independent trials, the probabilities of 1 and 2
successes are 0.4096 and 0.2048 respectively. Determine the distribution and write down
the probability of at least three successes.
15. In a binomial distribution with 6 independent trials, the probabilities of 3 and 4 successes
are found to be 0.1933 and 0.0644 respectively. Find the parameters ‘p’ and ‘q’ of the
distribution.
16. The probability that a teacher will given an unannounced test during any class meeting is
1/5. If a student is absent twice. What is the probability that he will miss at least one test?
17. Components are placed into bins containing 100. After inspection of a large number of
bins the average number of defective parts was found to be 10 with a standard deviation
of 3.

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