Probability & Statistics B.Tech Question Bank : tits.ac.in

Name of the College : Turbomachinery Institute of Technology &Sciences (TITS)
University : JNTU Hyderabad
Department : Computer Science Engineering
Subject Name : Probability and Statistics
Degree : B.Tech
Year/Sem : II/I
Website : tits.ac.in
Document Type : Question Bank

Download Model Question Paper : https://www.pdfquestion.in/uploads/djriet.edu.in/3048-psqb.pdf

TITS Probability & Statistics Question Paper

1. (a) Two marbles are drawn in succession from a box containing10 red, 30 white, 20 blue and 15 orange marbles,with replacement being made after each drawing. Find the probability that i. both are white ii. first is red and second is white

Related / Similar Question Paper : TITS B.Tech Data Warehousing & Mining Question Bank

(b) a businessman goes to hotels X, Y, Z ; 20% , 50% , 30% of the time respectively. It is known that 5% , 4%, 8% of the rooms in X, Y, Z hotels have faulty plumbing. What is the probability that businessmans room having faulty plumbing is assigned to hotel Z. [8+8]

2. (a) If A and B are events with P(A) = 1/3, P(B) = 1/4, and P(A U B) = 1/2, find i. P(A/B) ii. P(A \Bc )
(b) Three students A,B,C are in a running race. A and B have the same probability of wining and each is twice as likely to win as C. Find the probability that B or C wins.
(c) The students in a class are selected at random one after the other for an examination. Find the probability that the boys and girls are alternate if there are i. 5 boys and 4 girls ii. 4 boys and 4 girls.

3. (a) Define finite equiprobable space.
(b) Two cards are selected at random from 10 cards numbered 1 to 10. Find the probability p that the sum is odd if
i. The two cards are drawn together. ii. The two cards are drawn one after the other without replacement iii. The two cards are drawn are after the other with replacement

4. (a) The probability that a regularly scheduled flight departs on time is P(D) =0.83, the probability that it arives on time is P(A) = 0.82 and the probability that it departs and arives on time is P(D\A) = 0,78. Find the probability that a plane i. arives on time given that it departed on time and ii. departed on time given that it has arrived on time.
(b) One bag contains 4 White balls and 3 black balls and a second bag contains 3 white balls and 5 black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black?

5. (a) Define a random experiment, sample space, event and mutually exclusive events. Give examples of each.
(b) Box A contains 5 red and 3 white marbles and box B contains 2 red and 6 white marbles. i. If a marble is drawn from each box, what is the probability that they are both of the same color?

6. (a) If the probability that a communication system will have high fidelity is 0.81 and the probability that it will have high fidelity and high selectivity is 0.18. What is probability that a system will high fidelity will also have high selectivity.
(b) If the probability that a research project will be well planned is 0.80 and the probability that it will be planned and well executed is 0.72. What is the probability that a research project that is well planned will also be well executive.

7. (a) If P(A) = a, P(B) =b, P(A \ B) = c, express the following interms of a, b, and c i. P(Ac \ Bc) ii. P(Ac \ B) iii. P (Ac \ (A [ B)) iv. P[(AU(Ac \ B))] (b) Box A contains nine cards numbered 1 to 9 and box B contains five cards numbered 1 to 5. A box is chosen at random and a card is drawn, if the card shows an even number another card is drawn from the same box, if the card shows an odd number a card is drawn from the other box. i. What is the probability that both cards show even numbers? ii. If both cards show even numbers, what is the probability that they come from box A. iii.What is the probability that both cards show an odd number?

8. (a) Of the three men, the chances that a politician, a businessman or an academician will be appointed as a Vicehancellor (V.C.) of a University are 0.5, 0.3, 0.2 respectively. Probability that research is promoted by these persons if they are appointed as V.C. are 0.3, 0.7, 0.8 respectively. i. Determine the probability that research is promoted ii. If research is promoted, what is the probability that V.C. is an academician
(b) There are two boxes inbox I, 11 cards are there numbered 1 to 11 and in box-II, 5 cards numbered 1 to 5. A box is chosen and a card is drawn. If the card shows an even number then another card is drawn from the same box. If card shows an odd number another card is drawn from the other box. Find the probability that i. both are even ii. both are odd iii. if both are even. What is the probability that they are from box-I.

9. (a) If A and B are events with P(A) = 1/3, P(B) = 1/4, and P(A U B) = 1/2, find i. P(A/B) ii. P(A \Bc )
(b) Three students A,B,C are in a running race. A and B have the same probability of wining and each is twice as likely to win as C. Find the probability that B or C wins.
(c) The students in a class are selected at random one after the other for an examination. Find the probability that the boys and girls are alternate if there are i. 5 boys and 4 girls ii. 4 boys and 4 girls.

10. (a) If probability density function f(x) = kx3 in _ × _ 3 = 0 elsewhere Find the value of K and find the probability between x=1/2 and x=3/2.
(b) A random variable X has the following probability distribution. X: 1 2 3 4 5 6 7 8 f(x): K 2K 3K 4K 5K 6K 7K 8K Find the value of i. K ii. P(x _ 2) iii. P(2_ x _5).