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Probability

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  1. 101.A bag contains 6 blue and 6 green balls.
  2. 102.A candidate has to go to the examination centre using only one means of transportation out…
  3. 103.Three distinct numbers are selected randomly from the set 1,2,3,,40.
  4. 104.Two balls are selected at random one by one without replacement from a bag containing 4 wh…
  5. 105.If A and B are two events such that P(A B)=0.1, and P(A B) and P(B A) are the roots of the…
  6. 106.One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked …
  7. 107.A board has 16 squares (4 4 grid).
  8. 108.Let A=[a_ij] be a square matrix of order 2 with entries either 0 or 1.
  9. 109.Three defective oranges are accidentally mixed with seven good ones, indistinguishable by …
  10. 110.Let S be the set of all words formed by arranging all the letters of the word GARDEN.
  11. 111.Bag B_1 contains 6 white and 4 blue balls, Bag B_2 contains 4 white and 6 blue balls, and …
  12. 112.Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 bla…
  13. 113.Given three identical bags each containing 10 balls with different colour compositions.
  14. 114.A fair die is thrown until 2 appears.
  15. 115.Two integers x and y are chosen with replacement from the set 0,1,2,,10.
  16. 116.Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls.
  17. 117.Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15…
  18. 118.Three rotten apples are accidentally mixed with fifteen good apples.
  19. 119.A bag contains 8 balls, whose colours are either white or black.
  20. 120.Ajay will not appear in the JEE exam with probability p=27, while both Ajay and Vijay will…
  21. 121.Let N denote the number that turns up when a fair die is rolled.
  22. 122.Let be the sample space and A be an event.
  23. 123.Let M be the maximum value of the product of two positive integers whose sum is 66.
  24. 124.Let x,y be distinct integers with 1 x25, 1 y25.
  25. 125.Let N be the sum of the numbers obtained when two fair dice are rolled, and let the probab…
  26. 126.25% of the population are smokers.
  27. 127.Fifteen football players are given 15 T-shirts with their names on the back.
  28. 128.Let S=w_1,w_2, be a sample space with P(w_n)=P(w_n-1)2, n2.
  29. 129.If an unbiased die marked with -2,-1,0,1,2,3 is thrown five times, the probability that th…
  30. 130.A bag contains six balls of different colours.
  31. 131.A bag contains 6 balls.
  32. 132.Let A be the event that the absolute difference between two randomly chosen real numbers i…
  33. 133.In a binomial distribution B(n,p), the sum and product of the mean and variance are 5 and …
  34. 134.Two dice are thrown independently.
  35. 135.A pair of dice is thrown 5 times.
  36. 136.Three dice are rolled.
  37. 137.In a bolt factory, machines A, B, C manufacture 20%, 30%, 50% of the bolts respectively, w…
  38. 138.If P(X=x)=k(x+1)3^-x, x=0,1,2,3,, find P(X2).
  39. 139.Let N denote the sum of numbers obtained when two dice are rolled.
  40. 140.Let a die be rolled n times.
  41. 141.Let S=M=[a_ij], a_ij0,1,2, 1 i,j2 and A=M S: M invertible.
  42. 142.Let a biased coin have P(head)=14, tossed repeatedly until head appears.
  43. 143.Two dice A and B are rolled, giving ,.
  44. 144.A fair n-faced die (n>1) is rolled repeatedly until a number less than n appears.
  45. 145.A coin is biased so head is 3 times as likely as tail.
  46. 146.X B(n,p), mean - variance =1.
  47. 147.A bag contains 6 white and 4 black balls.
  48. 148.Let E_1,E_2 be events with P(E_1 E_2)=12, P(E_2 E_1)=34, P(E_1 E_2)=18.
  49. 149.A biased die is marked 2,4,8,16,32,32; probability of face n is 1n.
  50. 150.Five numbers x_1<x_2<x_3<x_4<x_5 are randomly selected from 1,,18 (increasing order).