PROBABILITY -03-ASSIGNMENT-PART-2

200. From a pack of 52 cards two cards are drawn in succession one by one without replacement. The probability that both are aces OR the probability that both are kings is (a) 2/13 (b) 1/51 (c) 1/221 (d) 2/21 201. A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is (a) 3/4 (b) 1/2 (c) 2/3 (d) 1/3 202. A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is (a) 1/8 (b) 1/12 (c) 1/2 (d) 1 203. A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is (a) (b) (c) (d) 204. A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one without replacement, what is the probability that all are white (a) (b) (c) (d) None of these 205. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is (a) (b) (c) (d) 206. For two events A and B, if and , then (a) A and B are independent (b) (c) (d) All of these 207. If and then (a) 1 (b) 0 (c) 1/2 (d) 1/3 208. From a pack of 52 cards two are drawn with replacement. The probability that the first is a diamond and the second is a king is (a) 1/26 (b) 17/2704 (c) 1/52 (d) None of these 209. The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is (a) 1/5 (b) 2/5 (c) 7/5 (d) 9/25 210. If E and F are independent events such that and , then (a) E and Fc (the complement of the event F) are independent (b) Ec and Fc are independent (c) (d) All of these 211. The probability of getting at least one tail in 4 throws of a coin is (a) 15/16 (b) 1/16 (c) 1/4 (d) None of these 212. If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7 is (a) 4/625 (b) 18/625 (c) 16/625 (d) None of these 213. A bag contains 4 white balls and 2 black balls. Another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, then the probability that both are white, is (a) 0.25 (b) 0.2 (c) 0.3 (d) None of these 214. A binary number is made up of 16 bits. The probability of an incorrect bit appearing is p and the errors in different bits are independent of one another. The probability of forming an incorrect number is (a) (b) (c) (d) 215. The probabilities of winning the race by two athletes A and B are and . The probability of winning by neither of them, is (a) (b) (c) (d) 216. Seven chits are numbered 1 to 7. Three are drawn one by one with replacements. The probability that the least number on any selected chit is 5, is (a) (b) (c) (d) None of these 217. A box contains 100 tickets numbered 1, 2.....100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability (a) (b) (c) (d) None of these 218. There are 20 cards. 10 of these cards have the letter ‘I’ printed on them and the other 10 have the letter ‘T’ printed on them. If three cards are picked up at random and kept in the same order, the probability of making word IIT is (a) (b) (c) (d) 219. Let A number is chosen at random from the set A and it is found to be a prime number. The probability that it is more than 10 is (a) (b) (c) (d) 220. A number is chosen at random from the numbers 10 to 99. By seeing the number a man will laugh if product of the digits is 12. If he choose three numbers with replacement then the probability that he will laugh at least once is (a) (b) (c) (d) 221. The probability that a married man watches a certain T.V. show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Then the probability that a wife watches the shows given that her husband does is (a) (b) (c) (d) 1 222. A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is (a) (b) (c) (d) None of these 223. A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one is red and other is black, is (a) (b) (c) (d) All of these 224. Two persons A and B take turns in throwing a pair of dice. The first person to through 9 from both dice will be avoided the prize. If A throws first then the probability that B wins the game is (a) (b) (c) (d) 225. An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is (a) 0.25 (b) 0.21 (c) 0.16 (d) 0.6976 226. If A and B are two events such that and then value of p so that is (a) 0.75 (b) 0.85 (c) 0.95 (d) 1 227. Eight tickets numbered 000, 010, 011, 011, 100, 101, 101 and 110 are placed in a bag. One ticket is drawn from the bag at random. Let A, B and C denote the following events: A – “the first digit is 0” B– “the second digit is 0” and C – “the third digit is 0”. then A, B and C are (a) Independent (b) Mutually exclusive (c) Mutually non-exclusive (d) Not independent 228. A die is rolled three times. Let denote the event of getting a number larger than the previous number each time and denote the event that the numbers form an increasing A.P., then (a) (b) (c) (d) 229. A reputed coaching employed 8 professors in the staff. Their respective probabilities of remaining in employment for three years are . The probability that after 3 years at least six of these still work in the coaching is (a) 0.15 (b) 0.19 (c) 0.3 (d) None of these 230. For a biased die the probabilities for different faces to turn up are given below Face: 1 2 3 4 5 6 Probability: .1 .32 .21 .15 .05 .17 The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1, is (a) 5/21 (b) 5/22 (c) 4/21 (d) None of these 231. A biased die is tossed and the respective probabilities for various faces to turn up are given below Face: 1 2 3 4 5 6 Probability: .1 .24 .19 .18 .15 .14 If an even face has turned up, then the probability that it is face 2 or face 4, is (a) 0.25 (b) 0.42 (c) 0.75 (d) 0.9 232. A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen to be white is [EAMCET 2003] (a) 2/15 (b) 7/15 (c) 8/15 (d) 14/15 233. A man draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is (a) 9/16 (b) 1/16 (c) 9/64 (d) None of these 234. For any two events A and B in a sample space (a) is always true (b) does not hold (c) , if A and B are disjoint (d) None of these 235. Three groups A, B, C are competing for positions on the Board of Directors of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. The probability that the new product will be introduced, is (a) 0.18 (b) 0.35 (c) 0.10 (d) 0.63 236. If and are the complementary events of events E and F respectively and if , then (a) (b) (c) (d) 237. Let A, B, C be three mutually independent events. Consider the two statements and and are independent; and are independent Then (a) Both and are true (b) Only is true (c) Only is true (d) Neither nor is true 238. In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is (a) 1/5 (b) 3/8 (c) 1/3 (d) 2/3 239. Let and . Then (a) (b) (c) (d) 240. It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they will win alternately is (a) (b) (c) (d) None of these 241. Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is (a) 1/2 (b) 7/18 (c) 3/4 (d) 5/12 242. The two friends A and B have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of A and B . The probability that all the tickets go to daughters of A is 1/20. The number of daughters each of them have is (a) 4 (b) 5 (c) 6 (d) 3 243. A bag contains coins. It is known that n of these have a head on both the sides, whereas the remaining coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 31/42, then the value of n is (a) 10 (b) 8 (c) 6 (d) 25 244. The letters of the word PROBABILITY are written down at random in a row. Let denote the event that two I’s are together and denote the event that two B’s are together, then (a) (b) (c) (d) 245. In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing, is (a) (b) (c) (d) 246. Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black balls respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, the probability that it is drawn from the first urn is (a) (b) (c) (d) 247. There are 3 bags, each containing 5 white balls and 3 black balls. Also there are 2 bags, each containing 2 white balls and 4 black balls. A white ball is drawn at random. The probability that this white ball is from a bag of the first group, is (a) 2/63 (b) 45/61 (c) 2/49 (d) None of these 248. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be hearts. Find the probability of the missing card to be a heart (a) (b) (c) (d) 249. One bag contains four white balls and three black balls and a second bag contains three white balls and five black balls. One ball is drawn from the first bag and placed unseen in the second bag. The probability that a ball now drawn from second bag is black is (a) (b) (c) (d) 250. A real estate man has eight master keys to open several new homes. Only one master key will open any given house. If 40% of these homes are usually left unlocked, the probability that the real estate man can get into a specific home if he selects three master keys at random before leaving the office is (a) (b) (c) (d) None of these 251. A coin is tossed 3 times by 2 persons. What is the probability that both get equal number of heads (a) 3/8 (b) 1/9 (c) 5/16 (d) None of these 252. A bag x contains 3 white balls and 2 black balls and another bag y contains 2 white balls and 4 black balls. A bag and a ball out of it are picked at random. The probability that the ball is white is (a) (b) (c) (d) None of these 253. The probability that in a year of the 22nd century chosen at random there will be 53 Sundays is (a) 3/28 (b) 2/28 (c) 7/28 (d) 5/28 254. If a coin be tossed n times then probability that the head comes odd times is (a) 1/2 (b) (c) (d) None of these 255. In a bolt factory, machines A, B and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their output 5, 4 and 2 percent respectively are defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found to be defective, the probability that it is manufactured by the machine B is (a) (b) (c) (d) 256. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter driver, car driver and a truck driver is 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver (a) (b) (c) (d) 1 257. From an urn containing 3 white and 5 black balls, 4 balls are transferred into an empty urn. From this urn a ball is drawn and is found to be white. The probability that out of the four balls transferred, 3 are white and 1 black is (a) (b) (c) (d) 258. In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct, given that he copied it, is 1/8. The probability that he knew the answer to the question, given that he correctly answered it, is (a) (b) (c) (d) None of these 259. A company manufactures T.Vs at two different plants A and B. Plant ‘A’ produces 80% and B produces 20% of the total production. 85 out of 100 T.Vs produced at plant A meet the quality standards while 65 out of 100 T.Vs produced at plant B meet the quality standard. A T.V. produced by the company is selected at random and is not found of meeting the quality standard. The probability that selected T.V. was manufactured by the plant B is (a) (b) (c) (d) None of these 260. A coin is tossed 3 times (OR Three coins are tossed all together). The probability of getting at least two heads is [MP PET 1995] (a) (b) (c) (d) 261. The probability of having at least one head in 3 throws with a coin is (a) 7/8 (b) 3/8 (c) 1/8 (d) None of these 262. A fair coin is tossed n time. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n is equal to (a) 15 (b) 14 (c) 12 (d) 7 263. The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is (a) (b) (c) (d) 264. In a binomial probability distribution, mean is 3 and standard deviation is . Then the probability distribution is (a) (b) (c) (d) 265. If X follows a binomial distribution with parameters and p and then (a) 1/2 (b) 1/4 (c) 1/6 (d) 1/3 266. The mean and variance of a binomial distribution are 6 and 4. The parameter n is (a) 18 (b) 12 (c) 10 (d) 9 267. Suppose X follows a binomial distribution with parameters n and p, where . If is independent of n and r, then (a) (b) (c) (d) None of these 268. If x denotes the number of sixes in four consecutive throws of a dice, then is (a) 1/1296 (b) 4/6 (c) 1 (d) 1295/1296 269. The probability that an event will fail to happen is 0.05. The probability that the event will take place on 4 consecutive occasions is (a) 0.00000625 (b) 0.18543125 (c) 0.00001875 (d) 0.81450625 270. A die is thrown three times. Getting a 3 or a 6 is considered success. Then the probability of at least two successes is (a) (b) (c) (d) None of these 271. Let p be the probability of happening an event and q its failure, then the total chance of r successes in n trials is (a) (b) (c) (d) 272. In tossing 10 coins, the probability of getting exactly 5 heads is (a) (b) (c) (d) 273. Assuming that for a husband-wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is (a) (b) 1 (c) (d) 274. The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers (a) (b) (c) (d) None of these 275. Three coins are tossed together, then the probability of getting at least one head is (a) 1/2 (b) 3/4 (c) 1/8 (d) 7/8 276. A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is (a) (b) (c) (d) 277. A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is (a) 8/3 (b) 3/8 (c) 4/5 (d) 5/4 278. A coin is tossed 10 times. The probability of getting exactly six heads is (a) 512/513 (b) 105/512 (c) 100/153 (d) 279. An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success (a) 4/27 (b) 8/27 (c) 16/27 (d) 24/27 280. The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is (a) 1458 × 10–5 (b) (c) (d) 281. If the probabilities of boy and girl to be born are same, then in a 4 children family the probability of being at least one girl, is (a) (b) (c) (d) 282. A committee has to be made of 5 members from 6 men and 4 women. The probability that at least one woman is present in committee, is (a) (b) (c) (d) 283. A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes (a) (b) (c) (d) None of these 284. A coin is tossed 4 times. The probability that at least one head turns up is (a) 1/16 (b) 2/16 (c) 14/16 (d) 15/16 285. If a dice is thrown twice, the probability of occurrence of 4 at least once is (a) 11/36 (b) 7/12 (c) 35/36 (d) None of these 286. In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is (a) 6 (b) 8 (c) 12 (d) 10 287. If two coins are tossed 5 times, then the probability of getting 5 heads and 5 tails is (a) (b) (c) (d) 288. 6 ordinary dice are rolled. The probability that at least half of them will show at least 3 is (a) (b) (c) (d) None of these 289. A fair die is tossed eight times. Probability that on the eighth throw a third six is observed is (a) (b) (c) (d) None of these 290. A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is (a) (b) (c) (d) None of these 291. The probability that a candidate secures a seat in Engineering through “EAMCET” is 1/10. 7 candidates are selected at random from a centre. The probability that exactly two will get seats is (a) (b) (c) (d) 292. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least three times is (a) 291/364 (b) 371/464 (c) 471/502 (d) 459/512 293. A fair coin is tossed 100 times. The probability of getting tails an odd number of times is (a) 1/2 (b) 1/8 (c) 3/8 (d) None of these 294. A coin is tossed 7 times. Each time a man calls head. The probability that he wins the toss on more occasions is (a) (b) (c) (d) None of these 295. A man draws a card from a pack of 52 cards and then replaces it. After shuffling the pack, he again draws a card. This he repeats a number of times. The probability that he will draw a heart for the first time in the third draw is (a) (b) (c) (d) None of these 296. A fair coin is tossed n times. Let X be the number of times head is observed. If and are in H.P., then n is equal to (a) 7 (b) 10 (c) 14 (d) None of these 297. Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total of 12 is (a) (b) (c) (d) 298. A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is (a) (b) (c) (d) None of these 299. A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is (a) 2 (b) 3 (c) 4 (d) 5 300. A box contains 24 identical balls, of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is (a) 5/64 (b) 27/32 (c) 5/32 (d) 1/2 301. A die is tossed twice. Getting a number greater than 4 is considered a success. Then the variance of the probability distribution of the number of successes is (a) (b) (c) (d) None of these 302. In order to get at least once a head with probability , the number of times a coin needs to be tossed is (a) 3 (b) 4 (c) 5 (d) None of these 303. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is (a) 0.8750 (b) 0.0875 (c) 0.0625 (d) 0.0250 304. In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is (a) 9/25 (b) 16/25 (c) 4/5 (d) 8/25 305. If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1, is (a) (b) (c) (d) 306. A die is tossed thrice. If getting a four is considered a success, then the mean and variance of the probability distribution of the number of successes are (a) (b) (c) (d) None of these 307. Suppose A and B shoot independently until each hits his target. They have probabilities 3/5, 5/7 of hitting the targets at each shot. The probability that B will require more shots than A is (a) 6/31 (b) 7/31 (c) 8/31 (d) None of these 308. A fair coin is tossed n times. Let X be the number of times head occurs. If and are in A.P., then value of n is (a) 7 (b) 10 (c) 12 (d) 14 309. In a precision bombing attack there is a 50% chance that any one bomb will strike the target. Two direct hits are required to destroy the target completely. The minimum number of bombs which should be dropped to give a 99% chance or better of completely destroying the target is (a) 10 (b) 11 (c) 12 (d) None of these 310. If the mean of a binomial distribution is 25, then its standard deviation lies in the interval given below [EAMCET 1992] (a) [0, 5) (b) (0, 5] (c) [0, 25) (d) (0, 25] 311. If n integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9 is (a) (b) (c) (d) None of these 312. A bag contains 14 balls of two colours, the number of balls of each colour being the same. 7 balls are drawn at random one by one. The ball in hand is returned to the bag before each new draw. If the probability that at least 3 balls of each colour are drawn is p then (a) (b) (c) (d) 313. An ordinary dice is rolled a certain number of times. The probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times. Then the probability of getting an odd number an odd number of times is (a) (b) (c) (d) None of these 314. The probability of a bomb hitting a bridge is and two direct hits are needed to destroy it. The least number of bombs required so that the probability of the bridge being destroyed is greater than 0.9, is (a) 8 (b) 7 (c) 6 (d) 9 315. All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spade comes. The probability that the ace comes in the 4th draw is (a) (b) (c) (d) None of these