SRM University 2007 B.Tech Bioinformatics BANK MA-262 (BIO – STATISTICS FOR BIO-INFORMATICS) - Question Paper

ques. BANK
MA-262 (BIO – STATISTICS FOR BIO-INFORMATICS)
UNIT : II PROBABILITY AND THEORETICAL DISTRIBUTIONS

PART - A
1. Define mutually exclusive events
2. Define Equally likely events
3. Define independent events
4. Define probability of an event
5. What is the chance that a leap year opted at random will contain 53 Sundays?
6. A bag contain three red, six white and seven blue balls. What is the probability that 2 balls drawn are white and blue?
7. For any 2 events A and B, prove that P(A ? B) = P (B) -P(A ? B)
8. State the legal regulations of Addition of probabilities for any 2 events.
9. State multiplication legal regulations of probability
10. Define conditional probability
11. If A and B are Independent events then prove that A & B are also independent events
12. If 2 dice are thrown, what is the probability that the sum is greater than 8.
13. Let A and B be 2 events such that P(A) = 3/4 and P (B) = 5/8 show that
(a) P (A?B) ? 3/4
(b) P (A?B) ? 5/8
14. State Baye’s theorem
15. Define a Random variable
16. Define distribution function and write any 2 properties.
17. Define Binomial Distribution
18. Comment on the following: the mean of binomial distribution is three and variance is 4.
19. In 256 sets of twelve tosses of a fair coin, in how many cases may 1 expect 8 heads and 4 tails?
20. Write the probability mass function of Poisson distribution
21. Six coins are tossed 6400 times. Using the Poisson distribution, obtain the approximate probability of getting 6 heads.
22. X is normally distributed and the mean of X is 12 and S.D is 4. obtain
(i) P (X ? 20) (ii) P (0 ? X? 12)
23. describe (i) Determinative (ii) Random Experiment with example.
24. describe (i) trial (ii) Event.
25. If A and B are independent Event P.T and are also independent Events.
26. If a surgeon transplants the kidney I 400 cases and succeeds in 160 cases, compute the probability of survival after operation?
27. From a pack of cards, 1 card is drawn at random what is the probability that is is either a king or a queen.
28. Write the probability mass for of Poisson distribution



PART -B
1. From 1st 25 numerals, 1 is drawn at random obtain the chance that (i) it is a multiple of five or seven (ii) it is a multiple of three or 7.
2. If 2 dice are thrown, what is the probability that the sum is (a) greater than eight (b) neither seven nor 11 ?
3. A and B alternately cut a pack of cards and the pack is shuffled after every cut. If A begins and the game is continued until 1 cuts a diamond elaborate the respective chances of A and B 1st cutting a diamond?
4. One shot is fired from every of the 3 guns. E1, E2, E3, denote the events that the target is hit by the first, 2nd and 3rd gun respectively. If P(E1) = 0.5 ,P(E2) = 0.6 and P(E3) = 0.8 and E1, E2, E3, are independent events, obtain the probability that (a) Exactly 1 hit registered (b) At lowest 2 hits are registered
5. A issue is provided to three students whose chances of solving it are 1/2 ,1/3, 1/4 what is the probability that (i) only 1 of them solves the issue (ii) the issue is solved.
6. Players X and Y roll a pair of dice alternately. The player who rolls 11 1st wins. If X begins obtain his chance of winning.

7. The contents of Urns I, II and III are as follows
three white, one black and one red balls
two white, four black and three red balls and
1 white, two black and three red balls

One Urn is chosen at random and From it 2 balls are drawn at random .If they are obtained to be one red and one black ball. What is the probability that the 1st urn was chosen.
8. In a factory machines A and B are producing springs of the identical kind. Of this production, machines A and B produce 5% and 10 % defective springs respectively machines A and B produce 40 % and 60% of the total output of the factory. 1 spring is opted at random and it is obtained to be defective what is the possibility that this defective spring was produced by machine A ?
9. An irregular 6 faced dice is such that the probability that it provide three even numbers in five throws is twice the probability that it provide two even numbers in five throws. How many sets of exactly five trials can be expected to provide no even number out of 2500 sets.
10. A manufacturer of cotter pins knows that five % of his Product is defective. If he sells cotter pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will fail to meet the guaranteed quality?
11. A car hire firm has 2 cars which it hires out day by day. The number of demands
for a car on every day is distributed as Poisson variate with mean 1.5 compute the
proportion of days on which (i) neither car is used and (ii) a few demand is refused.
12. In a distribution exactly normal, 7% of the items are under 35 and 89% are under 63
elaborate the mean and standard deviation of the distribution.
13. Of a large group of men, 5% are under 60 inches in height and 40% are ranging from 60
and 65 inches. Assuming a normal distribution, obtain the mean height and standard
deviation.
14. X is normal variable with mean 30 and S.D is 5. obtain the probability that
(i) P (X ? 26) (ii) P (X ? 45) (iii) P (X ? 40) (iv) P (/ X – 30 / ? 5)

Earning:   Approval pending.