Title MP DPP Sheet 30.pdf ✅

2 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 10. The probability that a certain machine will produce a defective item is 1/4. If a random sample of 6 items is taken from the output of this machine, what is the probability that there will be 5 or more defectives in the sample? (a) 3/4096 (b) 4/4096 (c) 18/4096 (d) 19/4096 11. If a fair coin is tossed 100 times and X is the number of heads obtained. The expectation value and variance of X are respectively (a) 25, 50 (b) 50, 25 (c) 50, 10 (d) 10, 50 12. A question paper contains 4 Multiple Choice Questions and a candiate will be declared to have passed the examination if he has answered at least one question correctly. The probability that the candidate passes the examination, is (a) 1/16 (b) 7/16 (c) 15/16 (d) 5/16 13. If a fair coin is tossed repeatedly, then the probability of getting m heads before n tails will be (a) 1 2 m n m n m         (b) 1 1 2 m n m n m          (c) 1 1 1 2 m n m n m           (d) 1 2 m n m n m         14. Suppose 60% of a herd of cattle is infected with a particular disease. Let Y = the number of non-diseased cattle in a sample of size 5. The distribution of Y is (a) binomial with n = 5 and p = 0.6 (b) binomial with n = 5 and p = 0.4 (c) binomial with n = 5 and p = 0.5 (d) none of these 15. A box contains n white and m red balls. If r balls are drawn at random with replacement, the expectation of getting white balls will be (a) m n m (b) n n m (c) nr n m (d) mr n m 16. A cricket player has to appear 4 times for a physical test.If the probability of passing the test is 2/3, then the probability that the player passes the test at least three times is (a) 16/81 (b) 16/27 (c) 8/81 (d) 16/81 17. In one dimension, a random walker takes a step of unit length, with equal probability to the left or right. What is the probability that the walker returns to the starting point after 6 steps? (a) 3/8 (b) 5/16 (c) 1/4 (d) 1/16 18. In one dimension, a random walker takes a step of unit length, with equal probability to the left or right. What is the probability that the walker returns to the starting point after 7 steps? (a) 3/8 (b) 5/16 (c) 1/4 (d) 0 19. A random walker takes a step of unit length along the right with probability 3/4 and a step of unit length along the left with probability 1/4. The mean displacement of the walker after 10 steps is (a) 2 units (b) 5 units (c) 10 units (d) 10 units 20. A random walker takes a step of unit length along the right with probability 3/4 and a step of unit length along the left with probability 1/4. The mean square displacement of the walker after N steps is (a)   1 3 4 N N  (b)   1 3 4 N N  (c)   1 1 4 N N  (d)   1 1 4 N N 