MATHEMATICS: PROBABILTY -ATUL KUMAR MOB 09310556579 ID-atul.mod@gmail.com,atul_eqn@rediffmail.com.,skypename--atul.kumar4 1. A bag contains 5 white and 3 black balls. Two balls are drawn at random. The probability that the drawn balls are of different colours, is equal to (a) 72 (b) 2815 (c) 73 (d) 74 2. The probability that at least one of the events A and B happens is 53. Probability of their simultaneous happening is 51. Value of ()()BPAP+is equal to (a) 52 (b) 54 (c) 56 ` (d) 57 3. One number is selected at random from first two hundred positive integers. The probability that it is divisible by 6 or 8, is equal to (a) 10029 (b) 10033 (c) 10043 (d) 41 4. Two fair and ordinary dice are rolled simultaneously. The probability of getting the sum of outcomes of the dice as a multiple of 4, is equal to (a) 95 (b) 41 (c) 91 (d) 31 5. Words are formed using all letters of the word PURUSHOTTAM. Probability that the formed word do not have similar adjacent letters, is equal to (a) 337 (b) 3319 (c) 3313 (d) 3323 6. Two fair and ordinary dice are rolled simultaneously. The probability that neither the sum of outcomes is 9 nor the dice show equal outcomes, is equal to (a) 98 (b) 91 (c) 1815 (d) 1813 7. The probabilities of happening of the events A and B are 41 and 21 respectively. If the probability of happening of A and B simultaneously is 507, then probability of neither A nor B happening, is equal to (a) 10039 (b) 41MATHEMATICS: PROBABILTY -ATUL KUMAR MOB 09310556579 ID-atul.mod@gmail.com,atul_eqn@rediffmail.com.,skypename--atul.kumar4 (c) 10011 (d) None of these 8. A five digit number (having all different digits) is formed using the digits 1, 2, 3, 4, 5, 6, 7, 9 and 9. The probability that the formed number either begins or ends with an odd digit, is equal to (a) 65 (b) 61 (c) 31 (d) 32 9. The probabilities of solving a problem by students A, B and C independently are 31,21 and 41 respectively. If they start solving the given problem independently, then the probability that atleast two of them will solve the problem successfully, is equal to (a) 245 (b) 249 (c) 247 (d) 2411 10. 20% bulbs in a set of 100 bulbs are defective. 5 bulbs are selected randomly from this set. The probability that the selected set has at least two and atmost 4 defective bulbs, is equal to (a) 5100180420380220CC.CC.C+ (b) 5100180420280320380220CC.CC.CC.C++ (c) 5100280320380220CC.CC.C+ (d) None of these 11. The probability that the persons P1 and P2 will die in a year are p and q respectively. The probability that at the end of the year only of them will be alive, is equal to (a) p + q – pq (b) p + q – p2 – q2 21625(c) p + q -2pq (d) pq (p +q –pq) 12. Two fair and ordinary dice are rolled simultaneously 4 times. The probability that both dice will show same outcome exactly twice, is equal to (a) (b) 3625 (c) 10825 (d) 7525 13. A fair coin is tossed repeatedly until the outcomes of both types have been obtained. The probability that the coin will be tossed exactly 5 times, is equal to (a) 161 (b) 321 (c) 21 (d) 41 14. Three numbers are chosen at random with out replacement from the set of integers {1, 2, 3, …….., 10}. The probability that the minimum of the chosen numbers is 3 or the maximum of the chosen numbers is 7, is equal to (a) 12023 (b) 12013MATHEMATICS: PROBABILTY -ATUL KUMAR MOB 09310556579 ID-atul.mod@gmail.com,atul_eqn@rediffmail.com.,skypename--atul.kumar4 (c) 6013 (d) 4011 15. A set is constructed randomoly, consisting of fifteen consecutive positive integers. Now two numbers are selected from this set simultaneously. The probability that the selected numbers will be odd, is equal to (a) 307 (b) 103 (c) 3014 (d) 152 16. Three integers are selected simultaneously from the set of integers {1, 2, 3, ……, 50}. The probability that the selected numbers are consecutive, is equal to (a) ()()49259 (b) ()()49256 (c) ()()49253 (d) None of these 17. Two numbers are selected simultaneously from the set {6, 7, 8, 9, ……., 39}. If the sum of numbers is even then the probability that both the selected numbers are odd, is equal to (a) 32 (b) 52 (c) 43 (d) 21 18. A bag contains 4 red, 5 white and 6 black balls. Three balls are selected from this bag simultaneously. The probability that one of the colour will be missing in the selected balls, is equal to (a) 455301 (b) 455366 (c) 455261 (d) None of these 19. Three children are selected at random from a group of 6boys and 4 girls. It is known that in this group exactly one girl and one boy belong to same parents. The probability that the selected group of children have no blood relations, is equal to (a) 151 (b) 1513 (c) 1514 (d) 152 20. P1 and P2 throw a fair coin in turn. One who gets a head first, wins the game, if P1 starts the game, probability that P232wins the game, is equal to (a) (b) 31 (c) 21 (d) 41 1—B 6—D 11—C 16—C 2—C 7—A 12—A 17—D 3—A 8—A 13—A 18—A 4—B 9—C 14—D 19—C 5—A 10—B 15—A 20—B