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Probability

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  1. 201.Players A, B alternately throw a pair of dice, starting with A.
  2. 202.A die thrown twice; sum observed is a multiple of 4.
  3. 203.Find the probability that a randomly chosen 5-digit number is made from exactly two digits…
  4. 204.Box I: cards 1--30.
  5. 205.E_1,E_2,E_3 pairwise independent, P(E_1)>0, P(E_1 E_2 E_3)=0.
  6. 206.Four fair dice thrown independently 27 times.
  7. 207.50% chance a bomb hits target; at least 2 hits needed to destroy.
  8. 208.Probability of a man hitting a target is 110.
  9. 209.Out of 11 consecutive natural numbers, three are selected at random.
  10. 210.P(A)=0.6,P(B)=0.4,P(C)=0.5; P(A B)=0.8, P(A C)=0.3, P(A B C)=0.2, P(B C)=, P(A B C)=, 0.85…
  11. 211.S=1,,20.
  12. 212.In a class of 60 students, 40 opted NCC, 30 opted NSS, 20 opted both.
  13. 213.A fair die rolled until two fours appear in succession.
  14. 214.A man wins Rs.100 for getting 5 or 6 on a die throw, loses Rs.50 otherwise.
  15. 215.Two integers selected at random from 1,,11.
  16. 216.A coin is tossed.
  17. 217.Probability of hitting a target is 13.
  18. 218.Two cards drawn successively with replacement from 52 cards.
  19. 219.An urn contains 5 red, 2 green balls.
  20. 220.A bag contains 30 white, 10 red balls.
  21. 221.Let A,B be non-null events with A B.
  22. 222.Find the minimum number of tosses of a fair coin so the probability of at least one head i…
  23. 223.Four persons hit a target with probabilities 12,13,14,18.
  24. 224.Two families, each with 2 children, boy/girl equally likely.
  25. 225.Find the minimum number of coin tosses so P(at least one head)>99%.
  26. 226.If three of the six vertices of a regular hexagon are chosen at random, find the probabili…
  27. 227.A candidate solves each of 50 problems correctly with probability 45.
  28. 228.X binomial with mean 8, variance 4.
  29. 229.A person throws two fair dice: wins Rs.15 for a doublet, Rs.12 for a sum of 9, loses Rs.6 …
  30. 230.Two families A, B with equal numbers of children.
  31. 231.Box A: 2 white, 3 red, 2 black.
  32. 232.A bag has 4 red, 6 black balls.
  33. 233.A,B,C pairwise independent, P(A B C)=0, P(C)>0.
  34. 234.Player X has a biased coin, P(head)=p; player Y has a fair coin.
  35. 235.For events A,B,C: P(exactly one of A,B)=P(exactly one of B,C)=P(exactly one of C,A)=14, an…
  36. 236.From 10 men, 5 women, 4-member committees with at least 1 woman are formed.
  37. 237.Two different numbers taken from 0,1,,10.
  38. 238.E,F independent; P(E F)=112, P( E F)=12.
  39. 239.P, Q, R try to hit a target independently with probabilities 34,12,58.
  40. 240.An unbiased coin tossed 8 times.
  41. 241.A box has 15 green, 10 yellow balls.
  42. 242.Two fair dice A, B thrown.
  43. 243.P(A)=25, P(A B)=320.
  44. 244.An experiment succeeds twice as often as it fails.
  45. 245.Triangle side lengths from three die throws.
  46. 246.12 identical balls placed in 3 distinct boxes.
  47. 247.X has 10 elements, P(X) its power set.
  48. 248.Mean and variance of a binomial variate X are 2 and 1.
  49. 249.A number x chosen from 1,,100.
  50. 250.Set S has 7 elements.