Title MP DPP Sheet 31.pdf ✅

1 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 CSIR-NET/JRF DEC 2023 (Online Batch) Section: MATHEMATICAL PHYSICS Daily Practice Problem (DPP) Sheet 31: PROBABILITY (Poisson Distribution & Gaussian Distribution) 1. If the probability of unfavorable reaction from a certain injection is 0.001, what is the probability that out of 2000 individuals, more than 2 will suffer from unfavorable reaction? (a) 2 5 e (b) 2 5 1 e  (c) 2 3 1 e  (d) 2 3 e 2. The chance of a coal miner being killed in a mine accident is 1/1400 during a calendar year. What is probability that a mine with 3500 employers will have at least one accident in a year? (a) 0.164 (b) 0.492 (c) 0. 618 (d) 0.918 3. A card is drawn from a well-shuffled pack of 52 cards. A sequence of 156 trials is made. What is the probability of getting a queen of clubs at least once? (a) 3 1 e (b) 3 1 1 e  (c) 52 1 1 e  (d) 52 1 e 4. Customer care of a mobile company receives on an average 4 calls per minute. The probability of receiving atmost 2 calls in a minute, is nearest to (a) 0.238 (b) 0.374 (c) 0.415 (d) 0.516 5. The average number of patients who arrive in a hospital per hour is 2. The probability that no patient arrives at the hospital in a day, is (a) 2 1 e (b) 2 24 e (c) 24 1 e (d) 48 1 e 6. Suppose flaws (cracks, chips, specks, etc.) occur on the surface of glass with density of 3 per m2 . What is the probability of there being exactly 4 flaws on a sheet of glass of area 0.5 m2? (a) 0.047 (b) 0.168 (c) 0.815 (d) 0.647 7. In a certain communications system, there is an average of 1 transmission error per 10 seconds. What is the probability of more than 1 error in a communication one-half minute in duration? (a) 0.2 (b) 0.32 (c) 0.56 (d) 0.8 8. If Delhi city has 2 accidents per day, how many accident-free days do you expect for the city in the year 2022? (a) 28 (b) 50 (c) 70 (d) 7