Mathematics - Probability

Question - 1

The probability that a leap year has 53 sundays

  • A \(\cfrac { 1 }{ 7 } \)
  • B \(\cfrac { 2 }{ 7 } \)
  • C \(\cfrac { 3 }{ 7 } \)
  • D \(\cfrac { 4 }{ 7 } \)

Question - 2

If A and B are two events such that \(P(A\cup B)=0.72\), \(P(A\cap B)=0.18\), and  \(P(\overline { B) } =0.9\), then P(A) equals

  • A 0.6
  • B 0.7
  • C 0.8
  • D 0.9

Question - 3

Thr probabilities of occurance of two events A and B are 0.25 and 0.5 respectively. The probability of their simultaneous occuring is 0.14; then the probability that neither of these occurs, is

  • A 0.21
  • B 0.27
  • C 0.35
  • D 0.39

Question - 4

The probability of a five-digit number formed by the digits 0, 1, 2, 3, 4 which is divisible by 4 is 

  • A \(\cfrac { 5 }{ 16 } \)
  • B \(\cfrac { 3 }{ 8 } \)
  • C \(\cfrac { 7 }{ 16 } \)
  • D \(\cfrac { 9 }{ 16 } \)

Question - 5

The probability that a teacher will give an unannounced test during any class is \(\cfrac { 1 }{ 5 } \). If a student is absent twice, the probability that he misses at least one test, is

  • A \(\cfrac { 16}{ 25 } \)
  • B \(\cfrac { 9 }{ 25 } \)
  • C \(\cfrac { 1 }{ 25 } \)
  • D NONE OF THESE

Question - 6

Out of (2n+1) tickets consecutively numbered, three are drawn at random. The probability that numbers are in A.P., is

  • A \(\cfrac { 1 }{ 4{ n }^{ 2 }-1 } \)
  • B \(\cfrac { 2 }{ 4{ n }^{ 2 }-1 } \)
  • C \(\cfrac { 3n }{ 4{ n }^{ 2 }-1 } \)
  • D \(\cfrac { 4n }{ 4{ n }^{ 2 }-1 } \)

Question - 7

The probabilities of A, B and C solving a problem are \(\cfrac { 1 }{ 2 } ,\cfrac { 1 }{ 3 } \) and \(\cfrac { 1 }{ 4 } \) respectively. They work independently. The probability of the problem being solved, is

  • A \(\cfrac { 1 }{ 2 } \)
  • B \(\cfrac { 3 }{ 4 } \)
  • C \(\cfrac { 1 }{ 24 } \)
  • D NONE OF THESE

Question - 8

a bag contains five white and three black balls. Four balls are drawn one by one without replacement. The probability that the balls are alternately of different colours, is

  • A \(\cfrac { 1 }{ 4 } \)
  • B \(\cfrac { 1 }{ 6 } \)
  • C \(\cfrac { 1 }{ 7 } \)
  • D \(\cfrac { 1 }{ 8 } \)

Question - 9

Out of n persons sitting in a row, the probability that two of the selected persons do not sit side by side, is

  • A \(\cfrac { 2 }{ n } \)
  • B \(1-\cfrac { 1 }{ n } \)
  • C \(1-\cfrac { 2 }{ n } \)
  • D None of these

Question - 10

Ten persons are sitting on a round table. The probability of three particular persons, sitting together, is

  • A \(\cfrac { 5 }{ 12 } \)
  • B \(\cfrac { 7 }{ 12 } \)
  • C \(\cfrac { 11 }{ 12 } \)
  • D \(\cfrac { 1 }{ 12 } \)
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