Book back answers and solution for Exercise questions - Maths: Probability Distributions: Binomial distribution: Problem Questions with Answer, Solution

**Exercise 7.1**

1. Define Binomial distribution.

2. Define Bernoulli trials.

3. Dedrive the mean and variance of
binomial distribution.

4. Write down the conditions for which
the binomial distribution can be used.

5. Mention the properties of binomial
distribution.

6. If 5% of the items produced turn out
to be defective, then find out the probability that out of 10 items selected at
random there are

(i) exactly three defectives

(ii) atleast two defectives

(iii) exactly 4 defectives

(iv) find the mean and variance

7. In a particular university 40% of the
students are having news paper reading habit. Nine university students are
selected to find their views on reading habit. Find the probability that

(i) none of those selected have news
paper reading habit

(ii) all those selected have news paper
reading habit

(iii) atleast two third have news paper
reading habit.

8. In a family of 3 children, what is
the probability that there will be exactly 2 girls?

9. Defects in yarn manufactured by a
local mill can be approximated by a distribution with a mean of 1.2 defects for
every 6 metres of length. If lengths of 6 metres are to be inspected, find the
probability of less than 2 defects.

10. If 18% of the bolts produced by a
machine are defective, determine the probability that out of the 4 bolts chosen
at random

(i) exactly one will be defective

(ii) none will be defective

(iii) atmost 2 will be defective

11. If the probability of success is
0.09, how many trials are needed to have a probability of atleast one success
as 1/3 or more ?

12. Among 28 professors of a certain
department, 18 drive foreign cars and 10 drive local made cars. If 5 of these
professors are selected at random, what is the probability that atleast 3 of
them drive foreign cars?

13. Out of 750 families with 4 children
each, how many families would be expected to have (i) atleast one boy (ii)
atmost 2 girls (iii) and children of both sexes? Assume equal probabilities for
boys and girls.

14. Forty percent of business travellers
carry a laptop. In a sample of 15 business travelers,

(i) what is the probability that 3 will
have a laptop?

(ii) what is the probability that 12 of
the travelers will not have a laptop?

(iii) what is the probability that
atleast three of the travelers have a laptop?

15. A pair of dice is thrown 4 times. If
getting a doublet is considered a success, find the probability of 2 successes.

16. The mean of a binomial distribution
is 5 and standard deviation is 2. Determine the distribution.

17. Determine the binomial distribution
for which the mean is 4 and variance 3. Also find P(X=15)

18. Assume that a drug causes a serious
side effect at a rate of three patients per one hundred. What is the
probability that atleast one person will have side effects in a random sample
of ten patients taking the drug?

19. Consider five mice from the same
litter, all suffering from Vitamin A deficiency. They are fed a certain dose of
carrots. The positive reaction means recovery from the disease. Assume that the
probability of recovery is 0.73. What is the probability that atleast 3 of the
5 mice recover.

20. An experiment succeeds twice as
often as it fails, what is the probability that in next five trials there will
be (i) three successes and (ii) at least three successes

**Answers:**

6. (a) 0.059 (b) 0.2642 (c) 0.0133 (d)
mean = 1 and variance = 0.95

7. (i) 0.01008 (ii) 0.00262 (iii)
0.09935

8. 0.375

9. 0.5767

10. (i) 0.3969 (ii) 0.45212 (iii) 0.9797
11. 5 or more trials

12. 0.7530

13. (i) 703 (ii) 516 (iii) 656

14. (i) 0.0634 (ii) 0.0634 (iii) 0.9729

15. 25/216 16.

16.

17. 3/4^{14}

18. 0.2626

19. 0.8743

20. (i) 80/243 (ii) 192/243

Tags : Problem Questions with Answer, Solution | Probability Distributions , 12th Business Maths and Statistics : Chapter 7 : Probability Distributions

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12th Business Maths and Statistics : Chapter 7 : Probability Distributions : Exercise 7.1: Binomial distribution | Problem Questions with Answer, Solution | Probability Distributions

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